Bologna UniversityPh.D. in Geophysi sXXI Cy leS ienti Se tor: GEO/10STUDY OF THE CIRCULATION PROCESSES IN THENORTHERN ADRIATIC SEA - COASTAL AREA ANDVENICE LAGOON INLETSDebora Bellaore

Ph.D. Coordinator: Tutor:Prof. Mi hele Dragoni Dr. Georg UmgiesserFinal Exam Year 2009

ContentsAbstra t viiiIntrodu tion 31 Phenomenology of the Northern Adriati Sea 51.1 Adriati Sea Morphologi al Chara teristi s . . . . . . . . . . . 51.2 Rivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3 Meteorologi al Chara teristi s . . . . . . . . . . . . . . . . . . 91.4 Tides, Surge and Sei hes in the Adriati Sea . . . . . . . . . . 101.4.1 Tides . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4.2 Storm Surges . . . . . . . . . . . . . . . . . . . . . . . 111.4.3 Sei hes . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.5 General Cir ulation . . . . . . . . . . . . . . . . . . . . . . . . 131.6 North Adriati Coastal Cir ulation . . . . . . . . . . . . . . . 142 Numeri al Modeling in the Northern Adriati Sea 172.1 Numeri al models des ription . . . . . . . . . . . . . . . . . . 172.1.1 POM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.1.2 ROMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.1.3 COHERENS . . . . . . . . . . . . . . . . . . . . . . . 222.1.4 NCOM . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.1.5 DieCAST . . . . . . . . . . . . . . . . . . . . . . . . . 232.1.6 SYSTEM3 . . . . . . . . . . . . . . . . . . . . . . . . . 242.1.7 MITg m . . . . . . . . . . . . . . . . . . . . . . . . . . 252.1.8 SHYFEM . . . . . . . . . . . . . . . . . . . . . . . . . 252.2 Setup Comparison . . . . . . . . . . . . . . . . . . . . . . . . 26

iv CONTENTS2.2.1 Numeri al Grid . . . . . . . . . . . . . . . . . . . . . . 262.2.2 2D and 3D Model Implementations . . . . . . . . . . . 292.2.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . 292.2.4 Initial Conditions . . . . . . . . . . . . . . . . . . . . . 322.2.5 For ings . . . . . . . . . . . . . . . . . . . . . . . . . . 323 SHYFEM Model 353.1 The equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2 Boundary and Initial Conditions . . . . . . . . . . . . . . . . . 373.3 Dis retization in time and spa e . . . . . . . . . . . . . . . . . 384 Test Cases - Pro ess Study in ideal basins 414.1 Baro lini Module . . . . . . . . . . . . . . . . . . . . . . . . . 414.1.1 Estuarine Outow Test Cases . . . . . . . . . . . . . . 414.2 Turbulen e Module . . . . . . . . . . . . . . . . . . . . . . . . 514.2.1 Kato-Phillips Test Case . . . . . . . . . . . . . . . . . 514.2.2 Deardor Test Case . . . . . . . . . . . . . . . . . . . . 545 Data Treatment and Model Input Preparation 575.1 Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.1.1 Histori al wind dataset analysis . . . . . . . . . . . . . 585.1.2 Wind database used as model input . . . . . . . . . . . 665.2 Tides and Currents . . . . . . . . . . . . . . . . . . . . . . . . 675.2.1 Tidal data . . . . . . . . . . . . . . . . . . . . . . . . . 675.2.2 The ow rate ADCP data . . . . . . . . . . . . . . . . 685.3 HF Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.4 Temperature and Salinity . . . . . . . . . . . . . . . . . . . . 706 Modeling Barotropi Pro esses 716.1 The 2D Simulation Setup . . . . . . . . . . . . . . . . . . . . . 716.2 Barotropi Simulation Results . . . . . . . . . . . . . . . . . . 746.2.1 Calibration of harmoni onstants . . . . . . . . . . . . 756.2.2 Water level validation . . . . . . . . . . . . . . . . . . 766.2.3 Flux data validation . . . . . . . . . . . . . . . . . . . 806.2.4 Residual Levels and Fluxes . . . . . . . . . . . . . . . . 85

CONTENTS v6.2.5 Extreme wind events . . . . . . . . . . . . . . . . . . . 887 Modeling Baro lini Pro esses 937.1 The 3D Simulation Setup . . . . . . . . . . . . . . . . . . . . . 937.1.1 Idealized For ing Simulations . . . . . . . . . . . . . . 937.1.2 Sensitivity Simulations . . . . . . . . . . . . . . . . . . 947.1.3 Realisti Simulation of the year 2004 . . . . . . . . . . 947.2 Baro lini Simulation Results . . . . . . . . . . . . . . . . . . 957.2.1 Idealized for ing impa t . . . . . . . . . . . . . . . . . 957.2.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . 987.2.3 Run of the year 2004 . . . . . . . . . . . . . . . . . . . 1008 Summary and Con lusions 109A The Arakawa Grids 113B Turbulen e Closure Models 117B.1 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117B.2 Turbulen e parameterization . . . . . . . . . . . . . . . . . . . 119B.2.1 Algebrai approa h . . . . . . . . . . . . . . . . . . . . 119B.2.2 1 equation models . . . . . . . . . . . . . . . . . . . . . 119B.2.3 2 equation models . . . . . . . . . . . . . . . . . . . . . 120Bibliography 124

vi CONTENTS

Abstra tThis work is a detailed study of hydrodynami pro esses in a dened area,the littoral in front of the Veni e Lagoon and its inlets, whi h are omplexmorphologi al areas of inter onne tion.A nite element hydrodynami model of the Veni e Lagoon and the Adriati Sea has been developed in order to study the oastal urrent patterns andthe ex hanges at the inlets of the Veni e Lagoon. This is the rst work inthis area that tries to model the intera tion dynami s, running together amodel for the lagoon and the Adriati Sea.First the barotropi pro esses near the inlets of the Veni e Lagoon have beenstudied. Data from more than ten tide gauges displa ed in the Adriati Sea have been used in the alibration of the simulated water levels. Tovalidate the model results, empiri al ux data measured by ADCP probesinstalled inside the inlets of Lido and Malamo o have been used and theex hanges through the three inlets of the Veni e Lagoon have been analyzed.The omparison between modelled and measured uxes at the inlets outlinedthe e ien y of the model to reprodu e both tide and wind indu ed waterex hanges between the sea and the lagoon.As a se ond step, also small s ale pro esses around the inlets that onne tthe Veni e lagoon with the Northern Adriati Sea have been investigated bymeans of 3D simulations. Maps of vorti ity have been produ ed, onsideringthe inuen e of tidal ows and wind stress in the area. A sensitivity analysishas been arried out to dene the importan e of the adve tion and of thebaro lini pressure gradients in the development of vorti al pro esses seenalong the littoral lose to the inlets. Finally a omparison with real datameasurements, surfa e velo ity data from HF Radar near the Veni e inlets,has been performed, whi h allows for a better understanding of the pro essesand their seasonal dynami s.The results outline the predominan e of wind and tidal for ing in the oastalarea. Wind for ing a ts mainly on the mean oastal urrent indu ing its de-ta hment oshore during Siro o events and an in rease of littoral urrents

during Bora events. The Bora a tion is more homogeneous on the whole oastal area whereas the Siro o strengthens its impa t in the South, nearChioggia inlet. Tidal for ing at the inlets is mainly barotropi . The sensi-tivity analysis shows how adve tion is the main physi al pro ess responsiblefor the persistent vorti al stru tures present along the littoral between theVeni e Lagoon inlets. The omparison with measurements from HF Radarnot only permitted a validation of the model results, but also a des riptionof dierent patterns in spe i periods of the year.The su ess of the 2D and the 3D simulations on the reprodu tion both ofthe SSE, inside and outside the Veni e Lagoon, of the tidal ow, through thelagoon inlets, and of the small s ale phenomena, o urring along the littoral,indi ates that the nite element approa h is the most suitable tool for theinvestigation of oastal pro esses. For the rst time, as shown by the uxmodeling, the physi al pro esses that drive the intera tion between the twobasins were reprodu ed.

Introdu tionThe work presented in this PhD Thesis is a detailed study of hydrodynami pro esses in the littoral area in front of the Veni e Lagoon and its inlets.The lagoon of Veni e is a omplex and unique environment both be ause ofthe internal hydrodynami s and the high variety in its morphologi al ha-ra teristi s. Be ause of the presen e of hannels, shallow ats and multiple onne tions with the open sea the lagoon is ontinuously hanging. For theseaspe ts the Veni e Lagoon and the oastal areas in front of it an be seen asa big laboratory for the study of hydrodynami pro esses.On the other hand, the area deserves its main importan e from the presen eof the ity of Veni e inside the lagoon. Many studies are driven by theneed to preserve this natural environment. In the last de ades, due to thein reased frequen y of the ooding events and to the deterioration of thewater quality, the ongoing resear h has been fo used to ontrol and preservethe hydrologi al, morphologi al and bio-geo- hemi al hara teristi s of thelagoon. Its onne tions with the open sea play a entral role and the studyof the mass balan e through the inlets is fundamental in order to monitorthe onservation of the lagoon itself.The ity of Veni e is an island situated approximately in the enter of thelagoon with other important islands in the southern and in the northernpart. The lagoon is onne ted to the Adriati Sea through three inlets thatguarantee the water ex hange with the open sea. The southern and the entral inlets (Chioggia and Malamo o, respe tively) are about 500 m wide,whereas the northernmost inlet (Lido) is nearly 1000 m wide. The averagedepth is around 8 m for Chioggia and 14 m for Malamo o and Lido.The inlets have undergone major hanges in the se ond part of the 19th andthe rst part of the 20th entury. Due to silting up of the entran es onlysmall boats ould pass in this period. Therefore jetties have been onstru tedthat rea h 2-3 km into the Adriati Sea and that gave the inlets the shapeand morphology that an nowadays be observed.To my knowledge, in the past no major studies have been arried out that

2 Introdu tiontry to measure or des ribe the ex hange and its me hanisms through theinlets. This might be surprising, onsidering the importan e of the inlets forthe maintenan e of the lagoon. Only re ently a major eort in this dire tionhas been undertaken, investigating the ex hange me hanism between thelagoon and the Adriati Sea, both by measurements of uxes and bio hemi alparameters at the inlets (Bian hi et al., 2004). Bottom mounted A ousti Doppler Current Prolers (ADCPs) have been installed at the three inletsand data have been analyzed (Ga£i¢ et al., 2002). With the data of theseeld ampaigns a hydrodynami model ould be validated. The modelingeort is presented in this work.In the re ent past, few modeling studies have been arried out to investi-gate the Sea-Lagoon water ex hange me hanisms. In parti ular in Umgiesser(2000) a rst attempt to understand the residual urrents due to the mostprominent wind regimes present in the Northern Adriati an be found. Anite element model (Umgiesser and Bergamas o, 1993, 1995) to simulatethe residual urrents of a omplete year (1987) is used there. The otherstudy (Bergamas o et al., 1998) applied the Prin eton O ean Model (POM)(Blumberg and Mellor, 1987; Mellor, 1991) to the lagoon and the oastal areaof the Adriati Sea to simulate both hydrodynami s and primary produ tion.Both approa hes suered from main de ien ies. Both models ould notbe validated with data be ause ux measurements were not available at theinlets. Moreover, the se ond study applied the POM model with a 1200 mgrid size, too oarse to resolve the important hydrodynami features of theVeni e Lagoon. On the other hand, the rst study used a alibrated modelfor the water levels inside the lagoon with good resolution of the hannelsystem (due to its nite element method), but failed to des ribe well theinterfa e dynami s, sin e the model domain ended exa tly at the inlets.The study of the internal dynami s of the intera tion hannels onne tingthe lagoon to the open sea is not the only obje tive of this work. The in-vestigation is also on erned with the Venetian littoral, identifying the mainpro esses that an be found and their intera tion with the inlets. To widenthe study area to the North-East Italian oast needs to onsider additionalfor ings and to put the lo al dynami s in relation with the general Adria-ti Sea urrents. Even if the tidal ee ts over the inlets an be onsideredbarotropi (Ga£i¢ et al., 2002), the presen e of many freshwater sour es alongthe oast and the hanging bathymetry lead to investigate both the horizon-tal and the verti al s ales. If baro lini pro esses are studied, as here, riverdis harge must be onsidered be ause the temperature and salinity gradient reated by the river dis harge starts to be ome an important for ing in thegeneral termohaline ir ulation. The idea is to hara terize the oastal hy-

3drodynami s, onsidering even the for ings that a t baro lini ally. A 3Dmodel formulation has been identied as the suitable tool to perform thisstudy. The small s ale horizontal stru tures that an form and persist alongthe venetian littoral will be studied in their dynami s.As a rst step, a des ription of the phenomenology of the Adriati Sea, witha dedi ated se tion for the nothern oastal area, is provided in the rst hap-ter. This is meant to explain and ontextualize the pro esses that will bestudied in this work. The se ond hapter will deal with the hoi e of numeri- al modeling as the suitable tool to inquire the hydrodynami s and a state ofthe art of model appli ations in the whole Adriati basin is drawn. SHYFEM(Shallow water HYdrodynami al Finite Element Model) will be des ribed in hapter 3, providing the numeri al hara teristi s and the advantages thatlead to the hoi e of this tool as the most suitable in the oastal and in-tera tion hydrodynami pro esses. Before the implementation in the studyarea, two modules, the baro lini and the turbulen e losure, will be he kedon a idealized basin performing some test ases (Chao and Boi ourt, 1986;Luyten et al., 1996; Bur hard, 2002) to ertify them. They are des ribedin hapter 4. The last three hapters deal with the model preparation andimplementation: hapter 5 des ribes the for ings hosen for the model setup; hapter 6 is devoted to treat the 2D model implementation to simulate thebarotropi lagoon-open sea intera tion pro esses, while hapter 7 presentsthe 3D model runs to identify the vorti al small s ale stru tures that o uralong the venetian littoral. Con lusions are drawn at the end.

4 Introdu tion

Chapter 1Phenomenology of the NorthernAdriati SeaThe Northern Adriati is a very interesting environment for hydrodynami studies and a number of physi al pro esses, widely ranging both the spa-tial and the temporal s ale, an be seen. To get to the heart the obje tivesof this work, a more general overview on the whole Adriati Sea phenome-nology is needed: the studied lo al s ale is inuen ed in dierent ways bythe more general topographi al, meteorologi al and hydrodynami hara te-risti s of the basin. All the following eviden es are the results of ampaignsand measurements, also ompared with modeling investigations, done in thelast twenty years to dene the state of the art of knowledge in the Adriati Sea.1.1 Adriati Sea Morphologi al Chara teristi sThe Adriati Sea is a semi en losed basin, onne ted with the MediterraneanSea by the Otranto Strait (Fig. 1.1). It extends latitudinally from 40 to 46degrees North. It an be divided, topographi ally, into three main areas: thenorthern part is hara terized by a shelf shallower than 40 m; the Jabuka Pit,280 m deep is present in the entral part of the basin, beeing deta hed fromthe deepest part of the Adriati Sea by the Palagruza Sill. The Southern arearea hes a depth of 1200 m in the so alled South Adriati Pit (Orli¢ et al.,1992). The se tion drawn along the Otranto Strait, dened as the Adriati

6 Phenomenology of the Northern Adriati SeaSea border, has an average depth of 325 m but it rea hes 780 m in its entralpart (Fig. 1.1).

Figure 1.1: Adriati Sea Map - Bathymetry, ridges and important morphologi alareas are shown. Harvard University Image.Two dierent typologies of oasts hara terize the eastern and western sidesof the Adriati Sea: several topographi al stru tures, like small islands, bays,estuaries and segmented ro ky oastlines, forms the ex Yugoslavia littoral.In this area, the bathymetry rea hes big depths, with an almost ompleteabsen e of the shelf. On the other hand, the western italian side is sandyand the depth in reases smoothly, parti ularly in the northern part of theAdriati (Fig. 1.1).The morphologi al onguration ontinues to hange there and fo used mo-nitoring has been done, parti ularly in the Adriati Northwestern oast, tostudy thoroughly its evolution: the reation and development of the so alledvenetian littoral has been histori ally re onstru ted by Gatto (1984). Cen-turies ago the onguration of the venetian drain basin was really dierentfrom now; many rivers, that nowadays ow dire tly into the Adriati Sea(Adige, Brenta, Piave), gave their ontribution to the water balan e of theVeni e Lagoon, owing into it. During the enturies the traje tory of theserivers were anthropogeni ally hanged to the present situation. The mainrivers, that are present in the North West oast of the Adriati Sea, inuen e

1.2 Rivers 7and modify its oastal morphology, bringing high quantities of sediments tothe open sea (Gatto, 1984). The Po river, whi h is the most important sour eof both sediments and freshwater in the North Adriati Sea, deserves somemore information. It ontributes to the oastline variation, parti ularly inthe Sa a di Goro, with the main a tion of the southern of its bran hes. Be- ause of the seasonal variations of its dis harge, dis ussed in the next se tion,it an bring sediments not only along the oast but also straight in the opensea in front of its estuary.1.2 RiversAlong the whole Adriati Sea oastline a number of rivers are present, withdierent estuarine stru ture and dimensions.Be ause of the interest in the hydrodynami s along the venetian oasts, as aprimary step, a des ription of rivers in the North-West littoral of the basin isgiven. The lo al impa t of freshwater inow into the basin starts to be omemeaningful when the baro lini pro esses are studied. The temperature andsalinity gradient, reated by the river dis harge, ontributes to the generalthermohaline ir ulation. The main rivers of this area are, following thelittoral from North, Isonzo, Tagliamento, Piave, Livenza and Sile; just Southof the Veni e Lagoon other two rivers, the Brenta and the Adige, ow intothe sea (Fig. 1.2).Even if these are all medium size rivers (average dis harge ranging from 40to 100 m3s−1), their ontribution to the oastal urrent annot be negle ted.The ombined ee t of these rivers and of the Po river indu es a y loni ir ulation in the northwestern shelves (Kourafalou, 2001).If the whole basin is onsidered, a omplete overview on the main riversdis harges, both on the western and on the eastern oast, is given by Rai i h(1994).Rai i h (1994) provides a sum of both the estimates of the freshwater dis- harge into the sea and of the hydrometri station measurements, on a sea-sonal times ale. Even if Rai i h (1994) does not give pre ise error bars, itis useful to dene the general trend: as an annual average the eastern rivers ontribute for the 45% of the total inow, while, on the western oast, thePo river alone overs the 28% of the dis harge. 19% omes from the severalrivers along the North-western littoral, our area of interest and the remain-ing 8% ows from the western littoral, South of the Po river (Rai i h, 1994).These values are variable during the year, with an in rease of the western

8 Phenomenology of the Northern Adriati Sea ontribution during winter (January and February) and of the Po river inthe early autumn (September 39%) (Rai i h, 1994). Also in springtime Po an rea h peaks over 4000 m3s−1 (Kourafalou, 1999).The Po river water outows during wintertime beeing onned in a oastalstrip of stratied freshwater, 10-20 km large (Kourafalou, 2001). As a on-sequen e, the area near the estuary is stratied during winter (MalanotteRizzoli and Bergamas o, 1983). During summer, the Po river water be omeswarmer than the basin water and it produ es a surfa e jet into the open sea.Two plumes develop, one to the Istrian oast and the other to the South.The latter sometimes reates an anti y loni surfa e gyre (Malanotte Rizzoliand Bergamas o, 1983; Zavatarelli et al., 2002).Models appli ations give some more detail on the prin ipal driving for es onne ted with the Po plume development: Kourafalou (2001) notes thatthe N-E winds onne the bulk of low salinity in the oastal band, redu ingstrati ation, while S-E winds in reases it, spreading freshwater oshore.

Figure 1.2: North Adriati rivers lo ation - the image is taken from Rai i h (1994).

1.3 Meteorologi al Chara teristi s 91.3 Meteorologi al Chara teristi sThe geographi al position of the Adriati Sea, in the Southern border ofthe Middle Europe, and the fa t that it is mainly surrounded by mountainsin the North-East border, inuen e the behaviour of wind and atmospheri pressure elds. The ombined ee t of the large s ale atmospheri pro essesand the lo al ee ts an be dete ted on ea h part of the basin.Globally there is a seasonally hanging inuen e of the Westerlies Belt andof the Sub Tropi al High Pressure Core: although the ee ts of the formerare seen throughout all the year, forming y loni and anti y loni distur-ban es, these stru tures tend to be strongly weakened by the a tion of theSub Tropi al High during the summer season. Also the oupled a tion ofthe I eland pressure low and the Eurasian pressure high, in winter, and theAzores high and the Kara hi low, in summer, ae t the dynami s of the area(Orli¢ et al., 1992).The presen e of planetary wave ee ts and long-term meteorologi al pre- onditioning ontribute in the extreme events formation: even if synopti and smaller s ale disturban es, ombined with tides, are responsible for ahigh per entage of water level peaks in the Northern Adriati , it has beendemonstrated that the simple a tion of planetary waves, that auses thelower-frequen y disturban es of the air pressure eld, is responsible of onethird of the sea level variability. This an be quantied in a sea level variationof 70 m, that o urs in ood events (Pasari¢ and Orli¢, 2001).Two main winds a t on the meso and lo al s ale: the Bora, proper of win-tertime, is a mainly dry wind that blows from North-East and it is reatedand dire ted by the big mountain hains of Cau asian Area. It deeply inu-en es the North Adriati dynami s (Orli¢ et al., 1992). The se ond wind isSiro o, a wet warm wind oming from South-East. It blows over the wholeAdriati Sea, bringing humidity, taken from the sea, to the northern part. Insummer, also the land-sea breeze along the oasts be omes important in thelo al dynami s (Orli¢ et al., 1992).The last aspe t ne essary to hara terize the meteorologi al behaviour of theAdriati Sea on erns with the solar radiation. Globally, the sea re eives400-500 J m−2day−1 in winter and 2200-2600 J m−2day−1 in summer (Orli¢et al., 1992). The temperature is generally warmer in winter in the North-West area, be ause of the shallower hara teristi s of the bathymetry.

10 Phenomenology of the Northern Adriati Sea1.4 Tides, Surge and Sei hes in the Adriati SeaTides, sei hes and surges are important pro esses in the Adriati Sea be ausethe parti ular shape of the basin and the shallow bottom of its northern endenhan es their ee ts. Before studying thoroughly the spe i ondition ofour study area, a small overview on these three pro esses has to be made.1.4.1 TidesThe Mediterranean Sea is a mi rotidal environment, usually with tides lessthan 50 m. Their a tion starts to be ome more important into the semien losed basin of the Adriati Sea, where 1 m of water displa ement an bere orded in the northern part (Tomasin and Pirazzoli, 1999). The behaviourof tidal urrents in the Adriati Sea has been investigated during the last entury: Polli (1960) stated that there are seven major harmoni omponentsthat des ribe the majority of the tidal signal. Three of them are diurnal (K1,O1, P1) and four are semidiurnal (M2, S2, N2, K2). More info in Tab.1.1The omponents M2, S2 and K1 are the more energeti in the NorthernHarmoni Components Origin Period [hM2 lunar prin ipal semidiurnal 12.42S2 solar prin ipal semidiurnal 12.00N2 lunar ellipti semidiurnal 12.66K2 lunar-solar de linational semidiurnal 11.97K1 lunar-solar de linational diurnal 23.93O1 lunar de linational diurnal 25.82P1 solar de linational diurnal 24.07Table 1.1: Name, origin and period of the seven major harmoni omponentsin the Adriati Sea.Adriati . These three sinusoidal signals develop dierently in the basin. K1shows otidal lines (lines where the tidal wave has the same amplitude),perpendi ular to the main basin axis. The K1 develops latitudinally, whileM2 and S2 have ir ular otidal lines around the amphidromi point in front

1.4 Tides, Surge and Sei hes in the Adriati Sea 11of An ona (Fig. 1.3). The M2 and S2 amplitude in reases approa hing the oast.The ombined a tion of the three main harmoni omponents produ es wavesthat develop along the oast as Kelvin waves (Mala£i¢ et al., 2000).The rst model appli ation of this work has pre isely the aim of re onstru t-ing the tidal urrents of the Adriati Sea, in parti ular in the study area infront of the Veni e Lagoon.

Figure 1.3: Harmoni onstants maps. The two main semidiurnal (M2, S2) andthe diurnal (K1) omponents of the Adriati Sea are shown.1.4.2 Storm SurgesFollowing the denition given by Fran o et al. (1982), in this work the term"storm surges" is used to dene the sum of for ed os illations and waterdisturban es mainly driven by wind events. Surges are typi al phenomena onne ted with the Adriati Sea, no external surges or earthquakes ee ts,like tsunamis, have been re orded in the last entury (Tomasin and Pirazzoli,1999). Surges are strongly onne ted with the shape of the basin and thisaspe t enhan es the ee t of South-Easterlies winds like Siro o.The ombined a tion of surges and astronomi al tides ontributes to the high

12 Phenomenology of the Northern Adriati Seawater displa ement that auses oodings along the northern oast and in thevenetian area.The storm surges tends to break the equilibrium status of the basin and theyare stri tly onne ted with the meteorologi al events. On the basis of theFran o et al. (1982) denition, even long term os illations (more than 10days), that are dete ted in the Adriati and that are due to the planetaryatmospheri os illation over the sea, an be onsidered "surges".1.4.3 Sei hesThe sei hes, on the other hand, are free stationary os illations, progressivelydumped by the external radiative energy and the internal fri tion (Tomasinand Pirazzoli, 1999).The sei hes a t bringing ba k the basin to ordinary onditions of equilibrium:they form as a rea tion to unstable onditions like a horizontal dieren e inwater level heights, due to the wind. In this ase periodi os illations o urand the period is determined by the topography, the horizontal dimensions,the basin depth and the number of nodes of the stationary wave (Tomasinand Pirazzoli, 1999). On the other hand, the amplitude is onne ted withthe speed and the dire tion of the wind.Sei hes are stronger in wintertime and in the Northern Adriati and lower insummertime and in the Southern Adriati (Fran o et al., 1982).The two major sei hes in the Adriati sea have periods of 21.2 and 10.8hours and they are generally onne ted with the presen e of Siro o wind orof frontal systems (Fran o et al., 1982). The rst sei he is the prin ipal one inthe basin and an be onsidered a uninodal os illation with the main node atthe meridional extreme of the sea and the antinode at the opposite end to theNorth (Tomasin and Pirazzoli, 1999). The se ond sei he is binodal, it uts thebasin into two areas with opposite phases and it propagates ounter lo kwisein the basin, as a semi diurnal tide (Tomasin and Pirazzoli, 1999). In the entral and northern part of the basin there are two more sei hes of period8.2 and 6 hours. Sei hes produ e an average level displa ement of 20-30 mbut an rea h 60-80 m and they have a quite long de aying time, around10-15 days (Fran o et al., 1982).

1.5 General Cir ulation 131.5 General Cir ulationThe study of oastal hydrodynami s annot negle t the importan e of large-small s ale pro esses intera tion, so an overview of the general ir ulation an help in understanding the phenomena present in the area of interest ofthis work.A stable surfa e y loni ir ulation is seen, with a northward ow along theeastern oast and a southward, summer strengthened, ow along the westernlittoral. The average velo ity is of 10 ms−1 but intera tion with oastalstru ture an enhan e it in some periods (Orli¢ et al., 1992).The net transport into the basin is of 0.1 Sv and the thermohaline for ing isseasonally driving part of the ir ulation: dividing seasonally the analysis ofthe Adriati Sea ir ulation, a general verti ally mixed pattern, in terms oftemperature, salinity and density, is seen during autumn and winter, Northto the Palagruza Sill (Fig. 1.1). The verti al homogeneity is driven mainlyby the surfa e heat in the Northern shallower areas (Malanotte Rizzoli andBergamas o, 1983; Orli¢ et al., 1992). The water olumn is homogeneousduring winter and stratied in summer, ausing the thermo-halo-py no sea-sonal y les (Fran o et al., 1982). In wintertime the surfa e ir ulation showsa y loni ir ulation both in the southern and entral areas of the basin witha strengthen Western Adriati Coastal Current (WACC). The North Adria-ti y loni gyre is wind driven during winter as well as the WACC, whi hows southward be ause of the oastal generated Kelvin waves propagation(Zavatarelli et al., 2002). During summer the baro lini a tion is predomi-nant, produ ing meanders in the WACC and inuen ing the North Adriati gyre (Zavatarelli et al., 2002; Artegiani et al., 1997b).In the Northern end, near the Gulf of Trieste there is the area of deep waterformation during the wintertime, aused by the old dry winds blowing fromNorth East (Bora wind). This water ows along the bottom, in a tongue thatfollows the western littoral, to the South. The ombined a tion of the densewater and of the freshwater oming from the Po river, drives the formationof the Winter North Adriati gyre (Malanotte Rizzoli and Bergamas o, 1983;Artegiani et al., 1997b).Dealing with the dense water formation, and the Adriati Sea is one of themajor sour es of it in the Mediterranean Sea, three kind of water masses anbe dened: the North Adriati Water (NAW), the Middle Adriati Water(MAW) and the Southern Adriati Water (SAW) (Orli¢ et al., 1992). Thewinter formation of NAW lls the Jabuka Pit and only a portion of it getsthrough the Palagruza Sill, rea hing the southern areas. In the Jabuka Pittthe MAW forms mixing with the NAW. This water is warmer and saltier and

14 Phenomenology of the Northern Adriati Seatends to stay longer in its origin area (Orli¢ et al., 1992). In the gyre presentin the South Adriati Pit the SAW an be dete ted after the winter oolingand it intera ts with the western oast NAW vein, along the isobaths, beingenri hed of oxygen (Orli¢ et al., 1992).Moreover, in the same area also the Modied Intermediate Levantine Water(MILW) is present. It is produ ed in the levantine basin and it is warmerand saltier than the SAW. It enters through the eastern part of the OtrantoStrait and it mixes with the denser water found there. The intera tion bet-ween these dierent water masses hanges not only seasonally but even in-terannually (Orli¢ et al., 1992; Oddo et al., 2005).1.6 North Adriati Coastal Cir ulationThe omplex hydrodynami system des ribed embeds a small s ale series ofphenomena along the oastline and here the fo us is on what happens in theNorth Western area, in the proximity of the Veni e Lagoon.On e more the inuen e of the Po river has to be onsidered be ause, ina way, its a tion inuen es the North entrapped ir ulation (Oddo et al.,2005). From modeling studies (Umgiesser and Bergamas o, 1998), the Poriver estuarine dynami s has been des ribed: the freshwater outow an havea dee tion to the North and then to South, in lo kwise dire tion, followingthe rules of potential vorti ity onservation. This phenomenon an intera twith the littoral ir ulation South of the Veni e Lagoon and there an beintera tions with the other two rivers present in the area, the Brenta andthe Adige. The big introdu tion of freshwater inje ted by the Po river doesnot inuen e dire tly the venetian littoral hydrodynami s but an enhan ethe open sea North Adriati gyre (Kourafalou, 2001). In summer a quitesigni ant northward oastal ow an be seen (Orli¢ et al., 1992).Near the Veni e Lagoon, the main large s ale pattern is the geostrophi southern urrent, whi h intera ts with the a tion of the three inlets of la-goon (Fig. 1.4). In fa t, the amount of water oming from the lagoon-opensea ex hange is bigger than that oming from the Po river: at the Malam-o o inlet (Fig. 1.4) a ow rate of 10000 m3s−1 is measured and, summing the ontribution of the three inlets, the total ow rate an rea h 24000 m3s−1,while the Po river shows an average dis harge rate of 1500 m3s−1 (Ga£i¢et al., 2002). Additionally the ombined a tion of tides and meteorologi- al for ings produ es interesting patterns whi h deviates the mean oastal urrent, reating meanders (Kova£evi¢ et al., 2004).

1.6 North Adriati Coastal Cir ulation 15

Figure 1.4: Satellite image of the Veni e Lagoon and the oastal area in front ofit. The three inlets of the lagoon, Lido, Malamo o and Chioggia, are shown.There is a rest in these meanders in the proximity of the Malamo o inlet(Paduan et al., 2003). The mean urrent tends to approa h the littoral Northto the inlet and then deviates oshore be ause of the shallow bathymetry(Gatto, 1984). The inlets tidal y les are typi ally of barotropi nature while,from HF Radar measurements, there is some indi ation that the surfa e urrent tends to be ae ted weakly by tides (20% of the total variability)4-5 km oshore (Kova£evi¢ et al., 2004). Then, in the oastal areas betweenthe inlets, some vorti al stru tures have been seen, on e more, from the HFRadar measurements. All these pro esses are the obje t of this PhD thesisand we will go deep in their des ription with the appli ation of the modelingtool in the next hapters.

16 Phenomenology of the Northern Adriati Sea

Chapter 2Numeri al Modeling in theNorthern Adriati Sea2.1 Numeri al models des riptionIn o eanography the investigation of hydrodynami pro esses is arried outby means of eld ampaigns, in situ measurements, moorings and satelliteimages as well as numeri al modeling. In re ent times modeling gained amajor role in the study of the ir ulation in the Adriati Sea, with severaldierent implementations and approa hes.The Adriati Sea has hydrodynami , morphologi al and meteorologi al ha-ra teristi s that render it a good lab for modeling studies both in terms ofpro ess studies and numeri al tests.In this hapter the dierent models re ently applied in the Adriati Sea orin some of its areas are presented. The aim is to stress the prin ipal nu-meri al hara teristi s, trying to explain some hoi es in the implementationand putting them in onne tion with the temporal and spatial s ales of thesimulated phenomena.The modeling areas are presented in Fig. 2.1. In Tab. 2.1 the model hara -teristi s are listed and they will be analyzed in the following paragraphs todraw a state of the art of numeri al modeling in the Adriati Sea.To better understand the numeri al hara teristi s of ea h model, more theo-reti al information is needed, therefore Appendix A is devoted to explain thedierent Arakawa Grids, usually applied in the o ean and atmospheri mo-

18 Numeri al Modeling in the Northern Adriati Sea

Figure 2.1: Areas of appli ation for the onsidered numeri al modelsdels, and the basis of the turbulen e losure s hemes is treated in AppendixB.2.1.1 POMThe Prin eton O ean Model (POM) (Blumberg and Mellor, 1987) is thebasis for a number of models developed and applied in the Adriati Sea. Thedieren es in the numeri s and the hoi es done in the dis retization mainlyidentify two models, the one des ribed in Bergamas o et al. (1999), and theone implemented by Zavatarelli and Pinardi (2003), Oddo et al. (2005) andOddo and Pinardi (2008). The details of the model applied by Zavatarelliand Pinardi (2003) are des ribed in Sannino et al. (2002).POM is a 3D, nite dieren e, free surfa e model. It applies the hydrostati and the Boussinesq approximations. Verti ally, a σ oordinates system isimposed, following the morphologi al stru ture of bathymetry:σ =

(z − η)

H + η(2.1)with z absolute layer depth, η water level surfa e displa ement, H total waterdepth. A higher density of levels an be imposed near the surfa e and thebottom, as done for the investigations in the Adriati Sea (Zavatarelli et al.,2002; Bergamas o et al., 1999).It uses a split mode time step, dividing it in external and internal modes.

2.1Numeri almodelsdes ription19

MODEL SCHEMES GRID LEVELS TURBULENCE CLOSURE SCHEMEPOM nite dieren es regular σ level hydrostati free surfa e Mellor-Yamada urvilinear orthogonalROMS nite dieren es urvilinear orthogonal oordinates hydrostati free surfa e Mellor-Yamadastret hed terrain following K-proleCOHERENS nite dieren es regular σ level hydrostati free surfa e algebrai expressions1-2 equation turbulen e energy modelsNCOM nite dieren es regular hybrid σ/z level hydrostati free surfa e Mellor-YamadaDieCAST nite dieren es regular z-level hydrostati rigid lid SYSTEM3 nite dieren es regular σ level non-hydrostati free surfa e MITg m nite volumes regular nite volumes non-hydrostati free surfa e kppSHYFEM nite elements unstru tured z-level hydrostati free surfa e K-ǫTable 2.1: Prin ipal hara teristi s of the models applied in the Adriati Sea.

20 Numeri al Modeling in the Northern Adriati SeaThe POM model solves the onservation of momentum equations, the on-tinuity equation and the tra er equations (T and S) using nite dieren ess hemes. No horizontal diusion is applied to the temperature and salinityelds (Zavatarelli and Pinardi, 2003). The equation of state for the densityis an adaptation of the UNESCO equation.The model parameterizes the momentum mixing, the temperature and sa-linity small s ale mixing with a horizontal diusion that depends on thehorizontal velo ity shear and on the grid step by the Smagorinsky algorithm(Sannino et al., 2002). The turbulen e losure is parameterized by the Mellor-Yamada 2.5 order turbulen e losure model (Mellor and Yamada, 1982) (seeAppendix B). The turbulent kineti energy, the turbulent length s ale andthe verti al velo ity shear permit to ompute the verti al mixing oe ients(Bergamas o et al., 1999).The models implemented by Zavatarelli and Pinardi (2003) (AIM-Adriati Intermediate Model and NASM - North Adriati Sea Model) and by Oddoet al. (2005) in the Adriati Sea introdu e dierent numeri al s hemes om-pared with the original POM applied by Bergamas o et al. (1999): theSmolarkiewi z (1984) s heme and the Clark's ux orre ted upstream s heme(Smolarkiewi z and Clark, 1986) are used to ompute the adve tion of tra- ers, instead of a entered dieren es s heme. The Clark's s heme is ha-ra terized by a small impli it diusion (Zavatarelli and Pinardi, 2003). This hoi e is driven by the need to orre tly ompute the tra ers in the Adriati Sea where high horizontal and verti al density gradients o ur due to thefreshwater input.2.1.2 ROMSROMS (Regional O ean Model System) is a free surfa e primitive equationmodel, based on the nite dieren es approa h. This model is a develop-ment of the S- oordinate Rutgers University Model (SCRUM). A part of thenumeri s has been rewritten to make it ompatible with the last generation omputer and to run it in a parallel mode. A more general des ription of theROMS model an be found on the web1.Verti ally it applies the stret hed terrain following oordinates to in reasethe spatial resolution in the interest areas. The formulation is the following:z = ζ + (1 +

ζ

h)[hcσ + (h− hcC(σ))] − 1 ≤ σ ≤ 0 (2.2)1http://marine.rutgers.edu/po/

2.1 Numeri al models des ription 21where h is the total depth, hc is either the minimum depth or the shallowerdepth above whi h more resolution is kept andC(σ) = (1 − b)

sinh(Θσ)sinhΘ +tanh[Θ(σ + 1

2)] − tanh(1

2Θ)

2tanh(12Θ)

(2.3)where 0 < Θ ≤ 20 and 0 ≤ b ≤ 1 are surfa e and bottom parameters(Haidvogel et al., 2000).Along the water olumn, entered se ond order nite dieren es are usedon a staggered grid. Higher order s hemes are not applied in the verti alto minimize the pressure gradient errors due to the higher sensitivity totopography. These errors are the result of the pressure gradient term splittinginto an along sigma omponent and a hydrostati orre tion.Horizontally the model uses orthogonal urvilinear oordinates on an ArakawaC grid (See Appendix A). Also for the zonal-meridional plane a se ond order entered nite dieren es s heme is applied.The hydrostati approximation is introdu ed and the momentum equationsare resolved with a split-expli it time-stepping numeri al s heme. This me-thod ouples the two modes, the baro lini and the barotropi ones, hoosinga smaller time step for the former one.The temporal dis retization is based on a third order predi tor (leap-frog)and a third order orre tor (Adam-Molton), to stabilize the omputation.The model has several options to dis retize the adve tion term: the se ond-fourth order entered dieren es or the third order upstream biased. Theses hemes are stable for the predi tor- orre tor approa h2.There is the opportunity to hoose dierent parameterizations: as an exam-ple, the horizontal mixing and the tra ers an be expressed on the verti allayers, on the geopotential surfa es or on isopy nal ones; the mixing an beharmoni or bi-harmoni .The applied turbulen e losure s heme an be either lo al or not lo al: theformer is based on the turbulent kineti energy equations proposed by Mellorand Yamada (1982) (Appendix B); the latter is based on the K-prole formu-lation, also for the surfa e and bottom layers. Additionally a wave/ urrentbed boundary layer s heme is used to identify the bottom stress and thesediment transport.2http://marine.rutgers.edu/po/

22 Numeri al Modeling in the Northern Adriati Sea2.1.3 COHERENSCOHERENS (COupled Hydrodynami al-E ologi al Model for Regional andShelf seas) is a 3D nite dieren e model that applies σ oordinates in ver-ti al (Eq. 2.1). It is a multi fun tion model applied mainly on oastal andshallow areas. It permits the oupling of dierent modules, dealing with thehydrodynami s, the e ologi al modeling and the water quality modeling.It applies the Boussinesq approximation to the momentum equation deningthe pressure terms as a ombination of an equilibrium part (barotropi ) anda deviation (baro lini ). Verti ally the hydrostati approximation is appliedand the baro lini pressure gradient term an be onsidered as an expressionof the buoyan y term (Marinov et al., 2006).The Joint Panel on O eanographi Tables and Standards equation is used todetermine the density (Fofono, 1985).COHERENS applies a two equation turbulen e losure s heme to omputethe eddy vis osity oe ients and the momentum equations: the eddy vis o-sity is dened from the turbulent kineti energy and the turbulent dissipationrate. The adve tion and diusion terms, the temporal derivative, the hori-zontal diusion and the sour e and sink terms are present in the momentumequations.The mode splitting approa h is used for the dis retization (Blumberg andMellor, 1987; Luyten et al., 1999). This te hnique onsists of a de oupledsolution of the barotropi part, for the verti al integrated momentum and forthe ontinuity equation, and of the baro lini part, for the momentum andthe s alar transport: a smaller time step is hosen for the barotropi part tosatisfy the stability riteria for the surfa e gravity waves. Longer timestepare hosen for the other terms.2.1.4 NCOMThe Navy Coastal O ean Model (NCOM) is POM based even if it introdu esa number of variations in the numeri al dis retization ompared with theoriginal version. Dierently from POM it uses a artesian horizontal grid.It is free surfa e, with a impli it treatment of the surfa e, and it applies thehydrostati and the Boussinesq approximations and the in ompressibility.It is a hybrid σ/z level model, that means that it uses σ oordinates for theupper layers and z oordinates for the lower ones and the model user andene the absolute depth where the σ to z swit h o urs.The horizontal pressure gradient term is treated on the σ layers as in the

2.1 Numeri al models des ription 23POM model (Blumberg and Mellor, 1987), while the momentum and s alars omputation is done with a quasi-third order upwind adve tion s heme (fors alars there is the opportunity to use the Flux-Corre ted Transport adve -tion s heme). The Coriolis term is omputed with a fourth-order interpo-lation and the horizontal pressure gradient with a fourth-order evaluation(Barron et al., 2006).The water density an be al ulated either with the polynomial approxima-tion of the equation of state proposed by Friedri h and Levitus (1972) or theUNESCO formula adapted by Mellor (1991).It permits to ompute the horizontal diusion with the Smagorinsky algo-rithm or with a grid- ell Reynolds number s heme, dening for both thes hemes a minimum value (Barron et al., 2006).For the verti al eddy vis osity omputation it introdu es the Mellor Yamadaturbulen e losure s heme (Pullen et al., 2003).The time dis retization is leap-frog and all the terms are omputed expli- itly ex ept for the free surfa e and the verti al diusion whi h are treatedimpli itly (Barron et al., 2006).2.1.5 DieCASTDieCast is a 3D nite dieren es model that applies z levels on the water olumn. This model was developed as a variation of the Sandia O ean Mod-eling System (SOMS) Model. It is based on primitive equations and appliesthe hydrostati and the Boussinesq approximations. It is rigid lid, that sim-plies the boundary ondition treatment. This aspe t is the main dieren ewith all the other models applied in the Adriati Sea (on the other hand alsothe MOM (Modular O ean Model) is rigid lid but it is applied on a widerspatial area - the Mediterranean Sea).This model is partially impli it and the main dieren e from SOMS is theappli ation of an Arakawa A grid, instead of a C grid. The reason of this hoi e is the smaller omputational weight for ea h timestep that permitsto maintain the stability even with a longer temporal timestep3. It is notvery dissipative be ause it applies a forth order numeri al s heme in spa eand a leap-frog dis retization in time, weakly ltered in the omputation ofthe dominant terms as the pressure gradient or the Coriolis term (Cushman-Roisin et al., 2005).The horizontal momentum, the potential temperature and the salinity are3http://www.ss .er .msstate.edu/DieCAST/

24 Numeri al Modeling in the Northern Adriati Sea omputed with ontrol volume averages. The verti al velo ity is derived fromthe in ompressibility equation (Cushman-Roisin et al., 2005). The vis osityand the horizontal diusivity are kept onstants 10 m2s−1; the verti al eddyvis osity is maintained at the order of 0.01 m2s−1.2.1.6 SYSTEM3SYSTEM3 is a 3D nite dieren e model based on the mass onservationand Reynolds equations (averaged Navier-Stokes).It introdu es the turbulen e ee ts, the variable density and the salinity andtemperature onservation equations adopting the UNESCO formula for thedensity omputation.It is a non-hydrostati model, therefore it onserves the full verti al momen-tum equation applying the arti ial ompressibility method (Chorin, 1967;Rasmussen, 1993). To avoid spurious ee ts in the hydrodynami pro essmodeling due to the appli ation of this method, the arti ial speed of soundintrodu ed into the ontinuity equation has to be kept higher than the elerityof surfa e and internal waves (Vested et al., 1998).The model adopts a staggered grid omputing the pressure, the temperatureand the salinity at the nodes, while the velo ity is omputed in points equidis-tant to nodes. The ontinuity equation is dis retized with spatial entereds hemes. The momentum equations are resolved impli itly with the ADI(Alternating Dire tion Impli it) algorithm, while the adve tion and diusionequations with QUICKEST (quadrati upstream interpolation for onser-vative kinemati s with estimated streaming terms) s heme, a onservative ontrol volume method.The turbulent ee ts are simulated omputing the verti al eddy vis osityeither with the k model, a one equation losure model, or with the k−ǫmodel,a two equation losure model (see Appendix B), or with the Smagorinsky subgrid model. In turbulen e losure models the treatment of buoyan y ee tsmust be onsidered: turbulen e buoyan y ee ts must be onsidered be ause,if not, in the presen e of density strati ation, whi h damps out the diusion,the entrainment and the mixing would be over-estimated. The Smagorinskysub grid model introdu es the buoyan y ee ts by means of the empiri alformula of Munk and Anderson (Vested et al., 1998).

2.1 Numeri al models des ription 252.1.7 MITg mThe MITg m model has been reated at MIT (Massa husetts Institute ofTe hnology, Boston) and it is based on the Navier-Stokes primitive equation,with a nite volume spatial dis retization that permits an easy re onstru tionof omplex bathymetries. The uxes are omputed in the normal dire tionswith respe t to the nite volume fa es (Marshall et al., 1997).It is a free surfa e model that applies the Boussinesq approximation. Theparti ularity of this model is the opportunity to start the non-hydrostati modality to identify small s ale hydrodynami stru tures, in relation withthe depth of the basin (Crise et al., 2003). It permits the appli ation ofdierent s hemes: entered dieren es for the horizontal diusion and theadve tion; impli it ba kward for the verti al diusion of the momentum andof the tra ers. The quasi-se ond order Adams-Bashfort s heme is applied forthe time dis retization (Crise et al., 2003).The horizontal turbulent ee ts are parameterized applying harmoni andbi-harmoni onstant oe ients for the turbulent vis osity and diusivity,while verti ally, the mixing and diusion pro esses an be parameterizedeither with harmoni onstant oe ients or with the k-pp se ond ordermodule. It permits to treat, separately on the water olumn, the surfa elimit layer and the internal layers.Also for the density omputation it is possible to adopt dierent hoi es: to onsider it linear or to adopt the state equation of UNESCO.This model is suitable to be used on parallelized platforms ( lusters).2.1.8 SHYFEMThe SHYFEM (Shallow water HYdrodynami al Finite Element Model) isthe model hosen to develop the work presented in this PhD Thesis. For thisreason a omplete hapter is devoted to the treatment of the new aspe ts andof the stru ture of this model. In this se tion the basi information onne tedwith previous works are enumerated to permit a omparison with the othermodels.SHYFEM is a 3D model, primitive equation based, whi h ombines the niteelement treatment with nite dieren e s hemes. The model applies z oordi-nates in the water olumn. Dierent numeri al s hemes are applied spatiallyand temporally. The water levels are des ribed with a pie ewise linear fun -tion and values are omputed at nodes. On the other hand, transports are entered in ea h element and des ribed with a onstant form fun tion on

26 Numeri al Modeling in the Northern Adriati Seathe element. Williams (1981) proposed an algorithm similar to the one usedfor this model, introdu ing onstant form fun tions for the velo ity. Theresulting grid is staggered. Transports for the zonal and meridional ompo-nents are omputed in the same point, the enter of the element, adoptinga type of Arakawa B grid on nite elements. The SHYFEM Model uses asemi-impli it time stepping algorithm to des ribe the time evolution of thevariables. It permits to eliminate the stability onstrains for the fast gravityand the Rossby waves.2.2 Setup ComparisonOn the basis of the given information, a preliminary omparison between thedierent models an be arried out, onsidering the dierent geographi alareas of appli ation in the Adriati basin. The grids and the hosen for ingswill be analyzed. Finally the results obtained by ea h model will be om-pared, dening the state of art of model development for the hydrodynami investigation in this spe i basin.2.2.1 Numeri al GridThe models presented in the previous se tions dier mainly in the typologyof grid and in the area of appli ation. Several models have been used tostudy the whole area of the Adriati Sea. Four appli ations are POM based- the system AIM-NASM developed by (Zavatarelli et al., 2002), the studydone by Oddo et al. (2005) and the implementation of Bergamas o et al.(1999) and NCOM (Pullen et al., 2003). The others are with DieCAST, de-s ribed in Cushman-Roisin et al. (2005) and ROMS (Sherwood et al., 2004).Under the umbrella of the EU Mediterranean Fore asting System Pilot Pro-je t (MFSTep) (Pinardi et al., 2003), the AIM (Adriati Intermediate Model)and the NASM (North Adriati Shelf Model) have been implemented on dif-ferent areas of the basin.The former applies a regular grid with an horizontal resolution of 1/20 ofa degree, around 5 km. It overs the basin from the northern end to 43.5degrees North, applying 21 verti al layers in σ oordinates. The latter isnested in the former with a regular grid of 1/37 of a degree (1.5 km), rotatedof about 67 degrees with respe t to the AIM grid. It overs the Northernarea of the basin (Fig. 2.2).On the other hand, DieCAST simply applies a high resolution regular grid,

2.2 Setup Comparison 27

Figure 2.2: Example of a regular grid - AIM (Adriati Intermediate Model) grid.Figure from (Oddo et al., 2005)

Figure 2.3: Example of a grid based on orthogonal urvilinear oordinates - AIMModel grid used in Zavatarelli et al. (2002).

28 Numeri al Modeling in the Northern Adriati Sea1/50 of a degree, over the whole basin. This hoi e is against the omputa-tional e onomy of the model but it permits to identify pro esses over a largerspatial range. The same approa h, with a 2 km regular grid on the wholebasin, is seen in the NCOM implementation.The ROMS Model approa h is more interesting, applying a grid based on or-thogonal urvilinear oordinates. It permits to in rease the spatial resolutionwhere there is the interest to resolve small s ale stru tures. An analogousgrid has been used for the AIM model in Zavatarelli et al. (2002) (Fig. 2.3).The opportunity to hoose dierent resolutions in spe i areas of the basinis also the advantage of using models like SHYFEM. It is based on an un-stru tured grid, whi h permits to rea h resolution down to tens of metersif needed. The SHYFEM grid, in the appli ations dis ussed in this stateof the art, has low resolution in the Southern part of the Adriati Sea butit in reases approa hing the oast, in the proximity of the Veni e Lagoon,where the hydrodynami pro esses of interest for this work an be dete ted(Bellaore et al., 2008). High resolution has been rea hed also in lo al ap-

Figure 2.4: SHYFEM Finite Element Grid.pli ations of other models, like the MITg m in the Gulf of Trieste (regulargrid with 250 m step - 88x128 ells) (Crise et al., 2003) or the COHERENS,applied in the "Sa a di Goro" (regular grid with 150 m step).Finally, SYSTEM3, whi h overs the Northern-Central area of the basin, has

2.2 Setup Comparison 29a lower resolution, 6 km, whi h is suitable to dete t the general ir ulationpattern.2.2.2 2D and 3D Model ImplementationsAll the models presented above are formulated in 3D. Notwithstanding this,some implementations done on the Adriati Sea, parti ularly the ones onlimited areas, are performed in 2D (i.e. SHYFEM Model, Veni e Lagoon).This aspe t shows how some elements lead to dierent hoi es, applying themodeling tool with a higher or lower degree of approximation on the ba-sis of the typology of pro esses and of the investigated areas. Generally,very shallow bathymetries does not need a deep verti al investigation of thewater olumn, be ause of the predominan e of mixing and barotropi hy-drodynami stru tures, therefore a 2D implementation is preferred. Thereare many morphologi al dieren es between the Northern and the Southernpart of the Adriati Sea: the North Adriati presents shallower bathyme-tries and the barotropi approximation is enough to reprodu e the majorityof ir ulation pro esses in limited zones like the Veni e Lagoon where thedepth is around 1 m (Cu o and Umgiesser, 2006). 2D runs are used for thereprodu tion of tidal urrents (Mala£i¢ et al., 2000; Bellaore et al., 2008)and also storm surge operational models an be ited as 2D implementations(Bajo et al., 2007).On the other hand, where thermohaline pro esses and strati ation ondi-tions be ome the study fo us, the 3D stru ture annot be negle ted (Bergamas oet al., 1999; Cushman-Roisin et al., 2005; Zavatarelli et al., 2002; Oddo et al.,2005).This remark is important when keeping in mind the main goal of this work.The oast in front on the Veni e Lagoon and, in parti ular, the three in-ter onne tion hannels, show a variety of hydrodynami pro esses of bothbarotropi and baro lini nature. Following a pro edure from low to high omplexity, the model implementations there will be both 2D and 3D.2.2.3 Boundary ConditionsThe dis ussion about boundary onditions permits the dis ussion of severalspe i modeling approa hes (nite dieren es - nite elements).In models that adopt regular grids, the in rease in spatial resolution is ob-tained by means of the nesting te hnique: it provides boundary and initial onditions to a high resolution model from an outer model, generally rougher

30 Numeri al Modeling in the Northern Adriati Seain resolution. This is what has been done in the implementation of AIM andNASM Models (Zavatarelli and Pinardi, 2003). AIM has also been nestedin OGCM (O ean General Cir ulation Model), development of the MOMModel, applied on the whole Mediterranean Sea. Nesting is based on thewater and heat transport balan e between the higher and lower resolutionmodels xing the boundary information on velo ity, temperature and salinityelds (Zavatarelli and Pinardi, 2003).A very re ent work by Oddo and Pinardi (2008) deals spe i ally with dif-ferent approa hes at the lateral open boundaries with a test implementationin the Adriati Sea. The rst approa h imposes the boundary onditions, oming from experimental data or models, as given values, like the Diri hlet ondition. The limit of this approa h is the possible in onsisten y betweenthe imposed values and the ones omputed inside the domain. Keeping thenesting approa h and trying to be onsistent at the lateral boundaries, anadditional te hnique, alled nudging, an be useful. A spatial variable on-dition, near the boundary, links the imposed values and the ones omputedby a relaxation time term, with a higher onstraint near the border and asmaller one advan ing further inside the domain. The boundary variable Θ isnudged with a referen e value ΘR. The formulation introdu es an additionalterm to the equation for Θ that readsΘ − ΘR

τ(2.4)where τ is the relaxation time that in reases further into the domain.Following the same philosophy, keeping a dened onstraint at the boundary,another approa h onsists in the variation of vis osity and diusivity in aborder strip, alled sponge layer (Oddo and Pinardi, 2008).A ompletely dierent approa h solves lo ally linearized primitive equationsof motion at the border, simplifying the physi s at the boundary (Oddo andPinardi, 2008).The radiation onditions, the adve tive onditions and the Flather onditionsare some examples.

• Radiation Condition: it imposes the internal elds on the boundaryby mean of a wave relation like∂Θ

∂t+ c

∂Θ

∂n= 0 (2.5)

c is the wave phase speed and n the normal dire tion. c an be imposed

2.2 Setup Comparison 31with dierent assumptions like the Orlanski one,c = −∂Θ

∂t(∂Θ

∂n)−1 (2.6)

• Flather Condition: it is a kind of radiation ondition that keeps themass onservation at the boundary (Oddo and Pinardi, 2008). It wasdeveloped for the rst time in tidal modeling and it puts in relationvelo ity and water elevation. Its formulation isV n

BTf = V nBTc −

√gH

H(ηc − ηf ), (2.7)where V n

BTc and ηc are the barotropi velo ity and the surfa e elevationof the oarse model, and V nBTf and ηf of the ne resolution model.

• Adve tive Condition: It is a ondition that adve ts the variableat the boundary with the normal velo ity provided by the imposedboundary values. The relation is∂Θ

∂t+ Vn

∂Θ

∂n= 0 (2.8)In the last implementations of the POM model the Flather ondition (Oddoand Pinardi, 2008) is applied, in NCOM as well for the elevation (Pullen et al.,2003). In NCOM the Orlanski radiation ondition is used for temperature,salinity and normal velo ity, while a zero-gradient ondition ontrols thetangential velo ity (Ro hford and Martin, 2001).The water surfa e is also a boundary and the models that onsider the massand heat ex hanges with the atmosphere need to impose further boundary onditions: this is the ase of POM, ROMS and NCOM implementations.In ROMS the treatment of the air-sea boundary is done applying the bulkparameterization proposed by Fairall et al. (1996), a kind of orre tion of thesurfa e momentum ux, sensible heat and latent heat. This level is used forthe one and two-dire tion nesting with the atmospheri models. ROMS hasalso an e ient data assimilation s heme.NCOM re eives information from the atmospheri model COAMPS and ap-plies the bulk formulas of Kondo (1975). Evaporation obtained from thelatent heat ux is used to ompute the surfa e salt ux and the COAMPSsolar radiation modies the water temperature on the layers.The POM implementation done by Zavatarelli et al. (2002) adopts the bulkformulas des ribed in Castellari et al. (1998).

32 Numeri al Modeling in the Northern Adriati Sea2.2.4 Initial ConditionsInitial onditions of temperature and salinity have been imposed for all themodels applied to the whole Adriati Sea basin (AIM, DieCAST, POM,SHYFEM, ROMS). Dierent datasets have been onsidered: the basi hoi ehas fallen on ATOSMOM dataset (Artegiani et al., 1997a; Zavatarelli andPinardi, 2003), whi h is the merge of two datasets, in luding data produ edby MOM in the Ionian Sea to initialize AIM. Then the AIM T/S data permitto initialize NASM Model.MOBD and ATOS2 databases have been used in DieCAST, to olle t higherresolution information in the oastal area (Cushman-Roisin et al., 2005).The implementation of POM by Bergamas o et al. (1999) is based on POEM1and POEM3 data, imposing horizontally uniform temperature and salinityproles (Artegiani et al., 1993).The same hoi e, in terms of T/S proles, has been applied for models onlimited areas like MITg m in the Gulf of Trieste (Crise et al., 2003).Another MIT gm implementation (ACOST1.1), under the ADRICOSM Pro-je t, stresses a dierent initialization te hnique, similar to the one of Zavatarelliet al. (2002), introdu ing T/S elds produ ed by a larger s ale model (ACOST1.2).Simpler initial onditions have been used to simulate the Veni e Lagoon ir ulation, in shallow water onditions. Unique typi al values of temperatureand salinity have been imposed on the whole basin.2.2.5 For ingsFor the Adriati Sea the more important for ings are wind, thermohalineuxes oming from the rivers and from the air-sea intera tion and the astro-nomi al tides.Trying to re onstru t realisti s enarios, wind elds are imposed from mo-dels: dierent dataset an be mentioned, like ECMWF (European Centre forMedium-Range Weather Fore asts), COAMPS (Coupled O ean-AtmosphereMesos ale Predi tion System) and LAMI (Limited Area Model Italy) (S iarraet al., 2006). In some appli ations, limatologi al for ings are hosen (Zavatarelliand Pinardi, 2003; Cushman-Roisin et al., 2005).Two works have been written trying to dene the variations in the ir ulationreprodu tion due to the dierent meteorologi al for ings hosen (Pullen et al.,2003; Signell et al., 2005). Pullen et al. (2003) applies the NCOM model oupled with the meteo model COAMPS. The oupling is tested with twodierent resolutions (36 km and 4 km). From this study a better apability of

2.2 Setup Comparison 33the high resolution model in the medium s ale wind phenomena reprodu tion(singular Bora events) is stressed (Pullen et al., 2003).The se ond work ompares dierent wind databases (ECMWF, LAMBO,LAMI e COAMPS) oupled with a wave model (SWAN) (Signell et al., 2005).The spatial resolution varies from 40 km (ECMWF) to 7 km (LAMI). On emore the best results are obtained with high resolution models. However aspe i ation has to be made: LAMI is partially deterministi and partiallysto hasti and it is suitable for simulation over long time ranges althoughit is a lo al model and it is strongly ae ted by boundary onditions. TheCOAMPS Model shows the same problem therefore, for real time simulations,global models like ECMWF are preferable, even if lower in resolution (Signellet al., 2005). The meteorologi al models generally provide all the variablesneeded to impose or ompute the surfa e heat uxes.The se ond for ing is river freshwater: it is introdu ed in Zavatarelli et al.(2002) and Oddo et al. (2005) as a limatologi al input, with a generali-zed information over the whole North-West littoral of the Adriati Sea. InZavatarelli et al. (2002) and Oddo et al. (2005) the only point sour e of fresh-water is the Po river, be ause of its entral role in the general ir ulation ofthe basin (Zavatarelli and Pinardi, 2003). On the other hand the ROMSModel onsiders dierent sour es of freshwater along the basin (Po and somerivers in Central Italy - Pes ara and Biferno). Data are imposed as meandaily averages.The Otranto Strait is onsidered open boundary in many model implementa-tions (POM, ROMS, SHYFEM, DieCAST). Zavatarelli and Pinardi (2003)imposes the OGCM nested uxes instead of S iarra et al. (2006) who ap-ply the ROMS Model spe ifying tidal levels and uxes produ ed by a model overing the whole basin.The SHYFEM Model imposes water level time series as open boundary on-ditions to reprodu e the tidal behaviour at the Strait.In this state of art it is useful to mention also that many tidal models havebeen developed and applied in the Adriati Sea (Mala£i¢ et al., 2000). Themodelled water levels an then be used as tidal for ings in the ir ulationmodels.

34 Numeri al Modeling in the Northern Adriati Sea

Chapter 3SHYFEM ModelSHYFEM is a nite element hydrodynami model developed at ISMAR-CNRIstituto di S ienze Marine. The 3D SHYFEM model has been implementedto simulate the lagoon-sea intera tion phenomena. The model, in the 2Dversion, has been applied in many studies to the Veni e Lagoon (Umgiesser,2000; Melaku Canu et al., 2001; Umgiesser et al., 2004; Cu o and Umgiesser,2006). It is a primitive equation model, based on the solution of the mo-mentum and ontinuity shallow water equations. In this work new aspe ts

Figure 3.1: SHYFEM Finite element grid of the Adriati Sea and the Veni eLagoon.

36 SHYFEM Model onne ted with the spatial dis retization and with the introdu tion in theequations of important terms for the 3D implementation, su h as the baro- lini pressure gradients, are presented. The other new aspe t that has to bestressed is that the model is implemented in 3D on a oupled basin, Adriati Sea-Veni e Lagoon, for the rst time. A nite element grid overing both theAdriati Sea and the Veni e Lagoon has been used with an in rease in spatialresolution around the inter onne tion areas (Fig. 3.1) rea hing resolution of30 m. This grid onsists of 15619 nodes and 28827 triangular elements.3.1 The equationsThe equations, integrated on ea h layer, read:∂Ul

∂t+ Advx

l − fVl = −ghl∂ζ

∂x− ghl

ρ0

∂

∂x

∫ ζ

−Hl

ρ′dz + (3.1)−hl

ρ0

∂pa

∂x+

1

ρ0(τ top(l)

x − τ bottom(l)x ) + AH(

∂2Ul

∂x2+∂2Ul

∂y2)

∂Vl

∂t+ Advy

l + fUl = −ghl∂ζ

∂y− ghl

ρ0

∂

∂y

∫ ζ

−Hl

ρ′dz + (3.2)−hl

ρ0

∂pa

∂y+

1

ρ0

(τ top(l)y − τ bottom(l)

y ) + AH(∂2Vl

∂x2+∂2Vl

∂y2)

∂ζ

∂t+

∑

l

∂Ul

∂x+

∑

l

∂Vl

∂y= 0 (3.3)where

Advxl = ul

∂Ul

∂x+ vl

∂Ul

∂yAdvy

l = ul∂Vl

∂x+ vl

∂Vl

∂y(3.4)with l indi ating the verti al layer, (Ul, Vl) the horizontal velo ities inte-grated over the layer (transports), (ul, vl) the velo ities in x,y dire tions, in

pa atmospheri pressure, g gravitational onstant, f Coriolis parameter, ζwater level, ρ0 the onstant water density, ρ = ρ0 + ρ′ water density, hl layerthi kness, Hl depth of the bottom of layer l, AH horizontal eddy vis osity.

3.2 Boundary and Initial Conditions 37The stress terms are expresses as followsτ top(l)x = ρ0ν

(Ul−1 − Ul)

(hl−1 + hl)/2τ bottom(l)x = ρ0ν

(Ul − Ul+1)

(hl + hl+1)/2(3.5)

τ top(l)y = ρ0ν

(Vl−1 − Vl)

(hl−1 + hl)/2τ bottom(l)y = ρ0ν

(Vl − Vl+1)

(hl + hl+1)/2(3.6)with ν verti al vis osity.

3.2 Boundary and Initial ConditionsThe boundary onditions for stress terms areτ supx = cDρawx

√

w2x + w2

y τ supy = cDρawy

√

w2x + w2

y (3.7)τ bottomx = cBρ0uL

√

u2L + v2

L τ bottomy = cBρ0vL

√

u2L + v2

L (3.8)cD is the wind drag oe ient, cB is the bottom fri tion oe ient, ρa is theair density, (wx, wy) is the wind velo ity and (uL, vL) is the bottom velo ity.The bottom drag oe ient cB is usually assumed to be onstant. However,in the ase of the Veni e Lagoon, it ould be dependent on the depth throughthe Stri kler formula

cB =g

C2C = ksH

1/6 (3.9)with C the Chezy oe ient and ks the Stri kler oe ient. Inside the la-goon dierent Stri kler oe ient have been used to distinguish the behaviorof hannels, tidal ats and the rest and at the three inlets slightly dierentvalues of this oe ient are used in inow and in outow onditions to pa-rameterize the unresolved physi al pro esses su h as the lo al head loss dueto sudden expansion of the out-owing water (Umgiesser et al., 2004).The model gives the possibility to impose both water level timeseries asopen boundary onditions or uxes. The se ond approa h is hosen to givethe information about river dis harge, while water levels are imposed at theOtranto Strait open boundary, as de ribed in Bellaore et al. (2008).3D Velo ity elds as initial ondition are set to zero while two options aregiven to impose initial temperature and salinity elds: there are either setto a onstant value over the whole basin or 3D matri es an be introdu ed.These two variables are given for ea h node and for ea h layer. They haveto be also imposed at the boundary for ea h layer.

38 SHYFEM Model3.3 Dis retization in time and spa eAs introdu ed in hapter 2, velo ities are omputed in the enter of ea helement, whereas s alars are omputed at ea h node. Verti ally the modelapplies Z layers with variable thi kness. Most variables are omputed in the enter of ea h layer, whereas stress terms and verti al velo ities are solvedat the interfa e between layers (Fig. 3.2).

Figure 3.2: Left gure: verti al stru ture - all variables but stresses are omputed in the middle of the layer. Right gure: nite element - s alars(as well as water levels) omputed at nodes and ve tors in the bari enters ofea h element.What on erns the temporal dis retization, the horizontal diusion, the baro- lini pressure gradient and the adve tive terms in the momentum equationare treated fully expli itly. The Coriolis for e and the barotropi pressure gra-dient terms in the momentum equation and the divergen e term in the on-tinuity equation are treated semi-impli itly. The adopted s heme is Crank-Ni holson. The semi-impli it treatment has to be onsidered a better hoi e ompared with the expli it approa h for long gravity waves with velo ityc =

√gH. In fa t semi-impli it s hemes are un onditionally stable with re-spe t to the gravity wave and are energy onserving. The bottom fri tionis treated fully impli itly. This is done be ause no problems onne ted withthe velo ity inversion, in the ases of big bottom stresses, an be avoided.

3.3 Dis retization in time and spa e 39Therefore the model is un onditionally stable what on erns the fast gravitywaves, the verti al stress and the Coriolis a eleration be ause of the hosentime dis retization (Umgiesser and Bergamas o, 1995).Moving to the spatial domain, the spe i approa h that is applied in SHYFEMmixes nite element stru ture and nite dieren es s hemes. Traditionallythe Galerkin formulation (Williams, 1981) has been applied on unstru turedgrid: pie ewise linear form fun tions are used to determine spatially the vari-ables. A variable ζ an be dened as a sum of these fun tions over the nodes.The form fun tions φm are 1 at the node m and 0 on the other nodes forea h element and linear inside ea h triangle.ζ = ζmφm m = 1...K (3.10)K is the number of nodes in the model domain.Unlu kily the Galerkin approa h does not give satisfa tory results if themodel treatment is semi-impli it, as it is in the SHYFEM Model. For thisreason the Galerkin approa h is still applied for the water levels omputationbut not for horizontal transports. To dis retize horizontal transports, not ontinuous, onstant fun tions ψm, dened over the whole domain are hosen.Their value is 1 at the element m and 0 on the rest of the basin. There is adis ontinuity at the border of the element. So transports an be denes asU = Unψn n = 1...J (3.11)with J total number of elements. Transports are dened in the enter of theelement, whereas s alars are omputed at nodes. The advantage in the adop-tion of this kind of formulation is onne ted with better properties of wavepropagation, geostrophi adjustment and total mass and energy onservation(Umgiesser and Bergamas o, 1995).The theoreti al basis of this approa h an be des ribed dening a lineardierential equation where L is the dierential operator

L(u) = 0. (3.12)Be ause it is impossible to ompute the exa t solution u, the approximationu is needed. It produ es a residual term R = L(u) that has to be minimized

∫

Ω

ΨnRdΩ =

∫

Ω

ΨnL(u)dΩ = 0 (3.13)where Ψn are the weight fun tions and Ω is the domain where the equationhas to be solved.

40 SHYFEM ModelAll the unknown and the spatially variable oe ients are developed in aseries of indipendent linear fun tions Φm, that are the form fun tions.u = Φmum m = 1...K (3.14)

K total number of nodes. Anyway the Galerkin approa h is used to hoosethe weight fun tions Ψn, whi h are dened equal to the form fun tions Φm.What is obtained is∫

Ω

ΦnRdΩ = 0 (3.15)The integral is onsidered a s alar produ t and R is posed orthogonal to thesub-spa e dened by the fun tions Φn. Introdu ing the linear developmentof u in the initial integral and remembering the linearity of the operator L,what results is anmum = 0, n=1,K and m=1,K, with anm =∫

ΩΦnL(Φm)dΩmatrix element of A = (anm).At the end of the pro edure the problem of solving this partial dierentialequation an be simplify to the solution of a linear equations system, withthe orre t boundary onditions (Umgiesser and Bergamas o, 1995).The appli ation of the semi-impli it algorithm leads to the formal solutionof the momentum equations for the transports and these are substituted inthe ontinuity equation. The obtained linear system has only water levels asunknowns in the nodes of the spatial domain. After the solution of this linearsystem, transports an be omputed dire tly from the momentum equations.For the omputation of the verti al diusivities and vis osities a turbulen e losure s heme is used. This s heme is an adaptation of the k-ǫ moduleof GOTM (General O ean Turbulen e Model) des ribed in Bur hard andPetersen (1999). Some theoreti al info in Appendix B.Be ause of the obje tive of this PhD work, the simulation of oastal andintera tion pro esses, two terms in the equations, the baro lini pressuregradient term and the turbulent diusion term, result very important. Themodules in whi h these terms are omputed have been he ked, hangedand developed, in order to be onfortable of their performan es in realisti alruns. In the next hapter and in Appendix B a des ription of numeri al hoi es in the dis retization and omputation of these terms and test asesare presented.

Chapter 4Test Cases - Pro ess Study inideal basins4.1 Baro lini ModuleThe study of oastal hydrodynami s requires the resolution of pro esses on-ne ted with river outow and other sour es of freshwater. The o urren eof temperature and salinity gradients due to the rivers a tion produ es hori-zontal and verti al variations in the density eld, as well as the evaporationand pre ipitation at the air-sea interfa e. These kind of pro esses are sim-ulated by means of the baro lini pressure gradient term in the momentumequations.In the past the real ase of Po river outow has been simulated applyinga previous version of the 3D SHYFEM Model (Umgiesser and Bergamas o,1998). Starting from that version, the baro lini pressure gradient termshave been developed and adapted to the version here tested.4.1.1 Estuarine Outow Test CasesIn order to test the model with the introdu tion of baro lini terms, three omputational test ases, proposed by Chao and Boi ourt (1986), were run.The estuarine dynami s is here simulated des ribing the dynami s of a fresh-water ow inje ted by means of a hannel into a regular basin. Even if inthe work of Chao and Boi ourt (1986) many ases are treated, the three test

42 Test Cases - Pro ess Study in ideal basins ases here presented are onsidered enough to dene the orre tness of thebaro lini pressure gradient term dis retization.

Figure 4.1: Verti al Se tion of the hannel onne ted with the ideal basin.Input Velo ity imposed at the open boundary.Before the explanation of ea h ase one aspe t has to be stressed: the Chaohydrodynami model is a rigid lid model and this means that only aseswhere the net water ux into the basin is 0 with no verti al water leveldispla ement an be treated to permit a omparison with SHYFEM, whi his free surfa e. The three test ases are run in an ideal re tangular basin,whi h is 60 km wide and 140 km long. A hannel, 15 km large and 52.5 kmlong, is onne ted to the basin along one of its borders. The whole basin is15 m deep (Chao and Boi ourt, 1986). Five verti al layers, whi h are 3 mthi k ea h, are imposed (Fig. 4.1).A 0.1 ms−1 freshwater inow velo ity is set at the open boundary upperlayers of the hannel onne ted to the ideal basin. Outow is set at thelower layers to obtain no barotropi ux at the open boundary (Fig. 4.1).The three test ases dier in the hoi e of verti al eddy vis osity and bottomfri tion values.

4.1 Baro lini Module 43

Figure 4.2: Chao Experiment 1 - Velo ity and salinity plots after ve days,rst layer

Figure 4.3: Chao Experiment 1 - Velo ity and salinity plots after ve days,fourth layer

44 Test Cases - Pro ess Study in ideal basins

Figure 4.4: Chao Experiment 1 - Velo ity and salinity plots after ve daysprodu ed by Chao and Boi ourt (1986), rst and fourth layerThe rst run setup onsiders bottom fri tion 0.01, verti al eddy vis osity 10E-4 m2s−1, horizontal diusion 10 m2s−1 and beta plane Coriolis approximationfor latitude 30 degrees North. After 5 days the velo ity and the salinity eldsare as presented in Fig. 4.2 and Fig. 4.3. These patterns are in agreementwith the results presented by Chao and Boi ourt (1986). To permit a visual omparison the gure obtained in Chao and Boi ourt (1986) is here shown inFig. 4.4. The velo ity and salinity values are of the order of the Chao resultsand this is a en ouraging result. After ve days the salinity gradients anbe seen lose to the hannel mouth, weakening from surfa e to bottom. Asexpe ted, a general dee tion of urrents to the South is seen.Observing the velo ity and salinity elds after 10 days, the results are still omparable with the Chao test even if the patterns are smoother than theoriginal ones (Figs. 4.5, 4.6, 4.7). In the Chao and Boi ourt (1986) testthe freshwater is spreading more oshore and, perhaps, some ee ts at theboundary opposite to the hannel an ae t the SHYFEM results.

4.1 Baro lini Module 45

Figure 4.5: Chao Experiment 1 - Velo ity and salinity plots after ten days,rst layer

Figure 4.6: Chao Experiment 1 - Velo ity and salinity plots after ten days,fourth layer

46 Test Cases - Pro ess Study in ideal basins

Figure 4.7: Chao Experiment 1 - Velo ity and salinity plots after ten daysprodu ed by Chao and Boi ourt (1986), rst and fourth layerThe same problem an be dete ted also in the other test ases but the stru -ture of the plume is omparable with the referen e one. The se ond experi-ment keeps the setup of the previous test but uses a higher verti al vis osityof 5 m2s−1 and the same bottom fri tion (0.01). What is expe ted is anin rease in the mixing ee ts and, in fa t, the same horizontal salinity gra-dients in the hannel an be seen both in the surfa e and in the fourth layerafter twenty days of simulation (Figs. 4.8, 4.9, 4.10).

4.1 Baro lini Module 47

Figure 4.8: Chao Experiment 2 - Velo ity and salinity plots after twentydays, rst layer

Figure 4.9: Chao Experiment 2 - Velo ity and salinity plots after twentydays, fourth layer

48 Test Cases - Pro ess Study in ideal basins

Figure 4.10: Chao Experiment 2 - Velo ity and salinity plots after twentydays produ ed by Chao and Boi ourt (1986), rst and fourth layerThe third and last experiment keeps the verti al eddy vis osity at 1 m2s−1but sets the bottom fri tion to zero. As a onsequen e of the absen e of fri -tion in the bottom layer some freshwater ngers an be dete ted in the fourthlayer. The same referen e bottom layer patterns from Chao and Boi ourt(1986) simulation (Fig. 4.13) are modelled by SHYFEM Model (Fig. 4.12),after 10 days. The surfa e layer shows a re ir ulation ell not really seenin the Chao results (Fig. 4.11). On e more it ould be onsidered as theinuen e of the eastern border of the ideal basin boundary.Considering the obtained results it an be said that the behaviour of SHYFEMin omputing the baro lini pressure gradient term is orre t and not ae tedby numeri al spurious ee ts.

4.1 Baro lini Module 49

Figure 4.11: Chao Experiment 3 - Velo ity and salinity plots after ten days,rst layer

Figure 4.12: Chao Experiment 3 - Velo ity and salinity plots after ten days,fourth layer

50 Test Cases - Pro ess Study in ideal basins

Figure 4.13: Chao Experiment 3 - Velo ity and salinity plots after ten daysprodu ed by Chao and Boi ourt (1986), rst and fourth layer

4.2 Turbulen e Module 514.2 Turbulen e ModuleThe verti al temperature and salinity proles, parti ularly near estuaries andsour es of freshwater, are mainly ontrolled by the turbulen e distribution inthe water olumn and by the verti al mixing (Bur hard and Petersen, 1999).Turbulent ee ts annot be negle ted in narrow hannels and in the onne -tion areas as the inlets of the Veni e Lagoon, where water an either havestratied or mixed verti al stru ture. Therefore the turbulen e ee ts mod-eling is not an easy task that requires the introdu tion of parameterizations,approximation and losure models, as better explained in Appendix B.To test the orre t omputation of the turbulen e ee ts in SHYFEM withthe implementation of the GOTM Turbulen e Closure Module, two test aseshave been studied.4.2.1 Kato-Phillips Test Case

Figure 4.14: Setup of the Kato-Phillips Experiment. Surfa e stress imposedon a verti ally stratied medium

52 Test Cases - Pro ess Study in ideal basinsThe rst test ase reprodu es the mixed layer deepening indu ed by a on-stant surfa e stress. This kind of ee t is due to the wind a tion on thesurfa e (Fig. 4.14). The wind mixing generally is reated by the turbulentkineti energy produ tion and the energy transfer onne ted with the wavebreaking (Bur hard and Petersen, 1999). Therefore the surfa e stress a tionis investigated along the whole water olumn initially stably stratied. Themodel is run in 1D, along the verti al oordinate. The visual omparison,in this test ase, is done between model outputs and the laboratory resultsobtained by Kato and Phillips (1969).This parti ular experiment has the property, in absen e of Coriolis for e, topresent self-similar solutions for the equation of motion and density whenthe strati ation prole is given by a power law of z, as in this ase (Luytenet al., 1996). Given a linear strati ation, the analyti al formula of the depthof the turbulent layer ish(t) = (2Ri)

1/4u∗(t/N0)1/2 (4.1)with the Ri hardson Number Ri = N2

0h2/U2, U mean value of urrent overthe turbulent layer.The initial onditions imposed at the water olumn are a onstant Brunt-Väisälä frequen y N0 10−2s−1 and a surfa e fri tion velo ity u∗ 10−2ms−1(Luyten et al., 1996). The applied Ri hardson number, homogeneous for selfsimilarity with the initial values of surfa e fri tion and buoyan y, is Ri 0.53.The hosen time step is 50 s and the verti al dis retization is 0.5 m. Thetotal depth of the water olumn is 100 m to avoid the bottom ee ts.In Fig. 4.15 the mixed layer evolution in time is shown. The abs issa is inthe adimensional unit tN0. As it an be seen, the trend is re onstru tedby the SHYFEM Model, omparing it with the results obtained by Luytenet al. (1996) (Fig. 4.15 entral panel) and by Bur hard and Petersen (1999)(Fig. 4.15 bottom panel). Bur hard and Petersen (1999) tested both thek-ǫ turbulen e losure s heme, whi h is also adopted in SHYFEM, and theMellor-Yamada s heme. More information about these two s hemes in Ap-pendix B.

4.2 Turbulen e Module 53

Figure 4.15: Kato-Phillips Experiment -The upper panel shows the evolutionin time of the turbulent layer from SHYFEM results, the entral is taken fromLuyten et al. (1996) and the bottom panel is from Bur hard and Petersen(1999). Bur hard and Petersen (1999) shows both the results applying thek-ǫ and the MY (Mellor-Yamada) turbulen e s hemes.

54 Test Cases - Pro ess Study in ideal basins4.2.2 Deardor Test CaseThe se ond test ase is the so alled Deardor experiment, whi h studiesthe mixed layer deepening by free onve tion. In this ase the investigatedee t over a stably stratied water olumn is the one produ ed by a bottominje tion of heat. The initial surfa e temperature is set to 22 degrees Celsius,with a de rease of 1 degree in 10 m. A 100 Wm−2 is inje ted from thebottom (Fig. 4.16). It has been impossible to ompare the absolute values

Figure 4.16: Setup of the Deardor Experiment. Constant heat ux fromthe bottom on a verti ally stratied medium.of the evolution of the temperature prole in time be ause the axis s alingapplied in Bur hard and Petersen (1999) are referred to the original paperfrom Deardor, not a essible. Therefore the visual omparison in trendswith the Bur hard and Petersen (1999) results is shown in Fig. 4.17. Evenif on a dierent s ale the temperature proles obtained with SHYFEM arereally similar to the ones from Bur hard and Petersen (1999), where boththe values omputed making use of the k-ǫ s heme and of the Mellor-Yamadas heme are shown. In any ase the two s hemes give identi al results in thistest.

4.2 Turbulen e Module 55

Figure 4.17: Deardor Experiment - The upper panel shows the temperatureproles at dierent times obtained from the SHYFEM Model, the bottompanel shows the results of k-ǫ and MY S hemes from Bur hard and Petersen(1999). The se ond graph uses s aled axis.

56 Test Cases - Pro ess Study in ideal basins

Chapter 5Data Treatment and Model InputPreparationThe implementation of a model to study the hydrodynami pro esses of a spe- i area is not only a mere appli ation of a numeri al tool but is also deeply onne ted with the availability of data both for the denition of for ings,initial, boundary onditions and for its validation. Knowing the behaviourof the prin ipal physi al variables in the study area permits to dene howto hoose input datasets to realisti ally reprodu e the phenomena. As ex-plained in hapter 1, the for ings that mainly inuen e the hydrodynami sin the Northern Adriati littoral in front of the Veni e Lagoon are winds,tides and temperature and salinity gradients. In the following se tions the hara teristi s of these variables are des ribed and information is given onthe available model or measurements datasets. All these aspe ts are at thebasis of modeling hoi es in terms of model grid setup and input preparation.5.1 WindThe meteorologi al ontribution an ae t strongly the dynami s of the waterex hanges at the lagoon inlets (Ga£i¢ et al., 2002). The residual water levelin the Adriati Sea and the related residual ow through the lagoon inlets aregenerated by the intense meteorologi al phenomena that o ur in this area.The rst step done is an analysis on histori al data to dene the spatialvariability of winds in the Veni e Lagoon. Afterwards the hosen modelinput is des ribed.

58 Data Treatment and Model Input Preparation5.1.1 Histori al wind dataset analysisSeveral meteorologi al stations have been installed inside the lagoon andin its proximity for a long time. Therefore an analysis of these stations an provide a spatial pattern overing more than one entury in time. Thestations onsidered here are Istituto Bio limatologi o and ITAV San Ni olóAirport lo ated on the Lido Island, ITAV Tessera Airport inland and theCNR O eanographi Platform 15 km oshore. These stations permit todes ribe the variable from oshore to inshore, perpendi ularly to the mainVeni e Lagoon axis (Fig. 5.1).

Figure 5.1: Lo ation of the analyzed meteorologi al stations: CNR Platform15 km oshore, Istituto Bio limatologi o and ITAV San Ni oló Airport onthe Lido Island, ITAV Tessera Airport inland.The majority of histori al data is in the Veni e Lagoon environmental databaseand an be downloaded from the Istituto Veneto website1.As a rst step, basi statisti s have been omputed (varian e, skewness andkurtosis) in order to understand if the data sets are homogeneous enoughto be merged into a unique data set. This pro edure is ne essary be ausethe three lo ations, CNR Platform, Lido and Tessera, have dierent types1http://www.istitutoveneto.it/venezia/

5.1 Wind 59of anemometers. The ITAV San Ni oló Airport and the Istituto Bio lima-tologi o databases are merged be ause sequential in time and be ause thetwo stations (Fig. 5.1) are not so far from ea h other. The same pro edurehas been adopted for the CNR Platform where both ISMAR and the Veni eMuni ipality olle ted data in dierent periods. The analyzed period rea hesfrom 12th of Mar h 1972 to 31th of De ember 1987 giving a wide temporal overage with few data gaps.In Fig. 5.2 the graph in the top shows a high varian e for the rst years of theperiod, probably onne ted with the large presen e of strong wind events.In the year 1983 there is a de rease in varian e, in orresponden e withthe hange of the instrument. The Veni e Muni ipality anemometer, thatmeasures from 1983, is lo ated in a higher position than the one from ISMAR.Moreover Cavaleri et al. (1984) state that the previous measurements wereinuen ed by the Platform stru ture. Therefore the two datasets an hardlybe onsidered part of the same population and this aspe t has to be takeninto a ount in the following analysis.The se ond graph of Fig. 5.2 evaluates the merging of the S. Ni oló Airportand the Istituto Bio limatologi o datasets. Ex luding the years 1977-1978,be ause of a la k of data, and two situations (1979 and 1986) where the highkurtosis value is due to extreme wind events, the rest of the timeseries ishomogeneous. The two datasets are onsidered part of the same population.The last graph of Fig. 5.2 shows the database of Tessera olle ted by theMilitary Air For e: on e more the o urren e of extreme events in 1986justies the high kurtosis seen for that year.For ea h lo ation the prin ipal wind speeds and dire tions are identied omparing them with the ones obtained by Pirazzoli and Tomasin (2002).In Fig. 5.3 Tessera and Lido data are expressed in fra tions of a degreewhereas the other data are with a unit degree variation. Wind dire tion, asusual in meteorology, is given as the dire tion of provenan e. The two mainwind regimes an be seen from these histograms: Bora wind from North-East and Siro o wind from South-East. The same pattern o urs in theTessera and CNR Platform stations, while Lido shows a high dire tionalvariability. Putting in relation the results shown in Fig. 5.4 and in Fig. 5.3,the high number of measured alm wind suggests that a lter over the lowspeed events an help in better dening the prin ipal wind dire tions. FromFig. 5.4 another aspe t has to be noted: the high frequen y of strong windevents re orded at the CNR Platform is due to the ISMAR anemometer thatsystemati ally overestimates the real wind speed (Cavaleri et al., 1984). Onthe other hand, the other two stations show a progressively attenuated windsignal approa hing the land: the mean speed for the CNR Platform is 8.16

60 Data Treatment and Model Input Preparation

Figure 5.2: Varian e, skewness and kurtosis graphs for the three lo ationsCNR Platform, Lido and Tessera.

5.1 Wind 61knots, for Lido it is 5.76 knots and for Tessera it is 4.01 knots. In Fig. 5.5also, the maximum, the 95% per entile and the mean values for the twosubsamples orresponding to Bora (provenan e dire tion in the range 0-90degrees) and to Siro o (provenan e dire tion in the range 90-180 degrees)are shown.

Figure 5.3: Wind Dire tion Histograms for the three lo ations: CNR Plat-form, Lido and Tessera.The speed and dire tion orrelation analysis between the stations an addinformation about the possible small s ale spatial variability of the wind.To perform this analysis only values every three hours have been onsideredbe ause the three timeseries have dierent sampling intervals (hourly vs 3hours). The orrelation has been omputed rst for the whole dataset butthe obtained values are not really signi ant (Tab. 5.1). The orrelation

62 Data Treatment and Model Input Preparation

Figure 5.4: Wind Speed Histograms for the three lo ations CNR Platform,Lido and Tessera.

5.1 Wind 63

Figure 5.5: Maximum, 95% per entile and mean values for the two subsam-ples orresponding to Bora Events (left olumn) and Siro o Events (right olumn)

64 Data Treatment and Model Input Preparation oe ients in rease if it is omputed only over the Bora subsample (Tab. 5.1).Correlation oe ients obtained onsidering the whole dataset or ltering thedata with speed lower than 5 knots are not substantially dierent stressinghow orrelation is better in semi alm regimes than during extreme events.During extreme wind events high errors in the dete tion of the real dire tion an arise be ause of the high dire tional variability so that the denitionof the Bora and Siro o subsamples an be a di ult task. This aspe t an explain the small orrelation oe ients omputed for the wind eventssubsamples. Both for the whole dataset and for the two subsamples, the CNRPlatform and the Lido stations are the best orrelated, be ause spatially losest.Table 5.1: Table of the orrelation oe ients for the whole set of data andfor the Bora and Siro o subsamples. Also the orrelation oe ients for thedatasets where speeds below 5 knots are ltered is shown.Corr CorrCoef Coefv<5knotsStations ALL BORA SIROCCO ALL BORA SIROCCOPtf-Lido 0.6071 0.6971 0.6599 0.5264 0.6599 0.6501Lido-Tes 0.6874 0.6601 0.5479 0.4365 0.5479 0.5057Tes-Ptf 0.5491 0.5937 0.5904 0.4256 0.5904 0.5458Moreover, the monthly average speed values have been omputed for theperiod Mar h 1961 - De ember 1987 to study possible trends. Fig. 5.6 showsthe monthly averaged values for Mar h, August and November. It stressesan attenuation of the signal in the re ent years, parti ularly for November inthe CNR Platform station. A more uniform behaviour is seen for the othertwo stations. No further trend analysis has been done be ause the period isnot long enough and with gaps in the timeseries.The average of the monthly averaged speeds have been omputed followingthe approa h of Pirazzoli and Tomasin (2002) to better dene the spatial hara teristi s of the wind eld. In Fig. 5.7, on e more, the progressiveattenuation of the signal going inshore is seen and the Lido and Tesserastations present the same trend. A dierent pi ture is seen for the CNRPlatform station during the winter months, whi h an be explained by theextreme events o urring espe ially in the open sea not rea hing the oast.

5.1 Wind 65

Figure 5.6: Monthly averaged value for ea h year for the three lo ations CNRPlatform, Lido and Tessera. The month of Mar h (upper panel), August(middle panel) and November (lower panel) are shown.

66 Data Treatment and Model Input Preparation

Figure 5.7: Average of the monthly averaged values over the period 1972-1987for the three lo ations CNR Platform, Lido and Tessera.5.1.2 Wind database used as model inputThe previous analysis about the lo al variability of the wind eld gives animportant information for the model input treatment. Wind and pressureelds over the whole Adriati Sea are the needed surfa e boundary for ings.The available wind elds are the 0.5x0.5 degrees T511 ECMWF (EuropeanCentre for Medium Weather Fore ast) 6 hours data.As previous studies pointed out (Cavaleri and Bertotti, 1996), these dataunderestimate the real meteorologi al status, espe ially in the Veni e Gulf,where the meteorologi al phenomena are more intense at the synopti s ale.In the last years various orre tion fa tors have been proposed for ECMWFwind elds over the Mediterranean sea, both in dire tion and speed. In thiswork a spatially variable orre tion fa tor provided by Cavaleri and Bertotti(1996) has been applied on the wind dataset used to for e the model. InCavaleri and Bertotti (1996) the orre ted wind elds have been omparedwith measured data in the CNR O eanographi Platform, 15 km oshore infront of the Veni e Lagoon (Fig. 5.1).The same orre tion mask has been adopted to set up an operational stormsurge nite element model at the Veni e Muni ipality (Bajo et al., 2007) withthe aim of fore asting the water level elevation generated by the meteorolo-gi al a tion (the residual water level). During this appli ation it has beenseen that it was not ne essary to apply the orre tion mask to the pressurebe ause it is orre tly reprodu ed by the ECMWF model over the whole

5.2 Tides and Currents 67basin (Zampato et al., 2005). The results obtained are in good agreementwith other fore ast models of the area.The introdu tion of the orre tion mask gives a ertain onden e on the orre t reprodu tion of the open sea wind eld in front of the Veni e Lagoon.Anyway, the previous analysis done on the wind variability going inshoregives the awareness that there is a dieren e lose to the oast between thereal winds and the input values introdu ed in the model. This aspe t will betaken into a ount trying to interpret the modeling results.5.2 Tides and CurrentsBe ause one of the goals of this work is the simulation of intera tion pro essesbetween the Venetian Lagoon and the open sea, a fundamental role is playedby the tidal for ing. ADCP measurements at the Lido inlet stress the majorrole of tides in the inow-outow y le (Ga£i¢ et al., 2002).In this work two dierent sets of measured data are used to alibrate andvalidate model results. The rst dataset onsists of the harmoni onstants(amplitude and phase) of the main tides that hara terize the sea surfa e ele-vation (SSE) of the Adriati Sea. For the lagoon inlets and for the OtrantoStation the harmoni onstants are omputed from available time series,ISMAR data for Lido and APAT (Environment Prote tion Agen y) datafor Otranto. The se ond dataset ontains the dis harge data through two ofthe three lagoon inlets measured by ADCP probes.5.2.1 Tidal dataThe Adriati sea is a basin hara terized by moderate tides. The highestamplitudes are found in the Northern sub-basin, extending from the line onne ting Pesaro to Kamenjak to the Northern oast (Fig. 3.1), where theamplitude of the M2 frequen y rea hes 0.266 m. Be ause of the impa t ofthis phenomenon in the area, tidal observations in the Northern sub-basinhave been olle ted from the middle of the 18th entury. Three relevantstations are present in the Northern part of the basin, Trieste, Venezia-Lido,Rovinj (Fig. 3.1), where the monitoring of tidal behavior overs more than a entury.Modeling the tidal urrents in the Adriati Sea means to be able to repro-du e the behavior of the seven main tidal onstituent in the basin, the foursemidiurnal ones M2, S2, N2, K2, and the three diurnal ones, K1, O1 and

68 Data Treatment and Model Input PreparationP1 (Polli, 1960). The knowledge about tides in the Adriati Sea derivesfrom previous works (Polli, 1960, 1961; Mosetti, 1987) where the main har-moni onstituents were derived analyzing the tide gauge measurements in anumber of stations along both the western and the eastern oast (Fig. 3.1).For what on erns the tides in the Veni e Lagoon, measured data of am-pli ation and delay of the main diurnal and semi-diurnal onstituents withrespe t to the Diga Sud Lido tide gauge are reported for many stations insidethe lagoon by Goldmann et al. (1975). This dataset has been onsidered forthe alibration of the model to reprodu e the tidal propagation in the Veni eLagoon (Umgiesser et al., 2004).Re ently, new harmoni onstants, al ulated from tide gauges time series,have been provided for the Veni e Lagoon by the Environment Prote tionAgen y APAT (Ferla et al., 2007). In the same paper even an a urateanalysis on long term variations in the tidal regime in the Veni e Lagoonhas been presented. From this data set the harmoni onstants for the Lidostation has been derived.From a omparison between the ited papers, the two sets of harmoni on-stants omputed for the lagoon are signi antly dierent and the main hy-pothesis is the inuen e of the deep morphologi al hanges o urred in thelast entury (Ferla et al., 2007).5.2.2 The ow rate ADCP dataRe ent ampaigns in the area of interest provide ADCP data for years 2001-2002. The aim of these measurements is to study the time-dependent vari-ability of the inlet urrents as well as of water ex hange rates. The urrentdata have been olle ted using bottom-mounted ADCPs installed in ea h in-let. Current speed and dire tion along the water olumn are re orded every10 minutes with a verti al resolution of 1 meter in sele ted lo ations insidethe inlets.During a preliminary phase, measurement ampaigns have been arried outto estimate the relationship between the verti ally averaged water velo ity olle ted by the xed ADCP and the inlet ow rate. About 100 ship-borneADCP surveys were ondu ted to estimate the water inow and outowthrough ea h inlet both during spring and neap tide.Comparing the dis harge results with the verti ally averaged velo ity ol-le ted by the bottom mounted ADCP for the same period, the parametersof a linear orrelation fun tion have been al ulated (Ga£i¢ et al., 2004).Therefore, the ow rate is available every 10 minutes applying the al ulated

5.3 HF Radar 69linear regression formula to the verti ally integrated measured urrent values(Ga£i¢ et al., 2002).5.3 HF RadarThe HF Radar dataset of surfa e urrents is used for the omparisons withsimulations. The dataset is the result of re ords taken by three antennas,two of them lo ated along the oast near the Veni e Lagoon in Lido andin Pellestrina and one at the CNR O eanographi Platform, lo ated 15 kmoshore (Fig. 5.8). The spe i des ription of the olle tion of data andtheir analysis an be found in Kova£evi¢ et al. (2004). In this work the useddata are hourly values, low-pass ltered, to eliminate the inuen e of inertialfrequen ies, and detided, to permit the analysis of residual urrents (Kova£e-vi¢ et al., 2004). The HF Radars installed in the littoral area in front ofthe Veni e Lagoon have an e ien y angle where the radial measurement isnot ae ted by high errors, in the range of 30-150 degrees. Along the idealline that onne ts the antennas there is a so alled blind area where mea-surements annot be onsidered orre t, be ause of signal refra tion ee tsand propagation loss (Kova£evi¢ et al., 2004). After post pro essing (thatin ludes the elimination of spikes) the HF Radar data are interpolated ontoa regular grid with grid size of 750 m.

Figure 5.8: Maps of the HF Radar overage in the proximity of the Veni eLagoon. Two of them are lo ated on the Pellestrina and Lido Islands, thethird is at the CNR Platform. Codar HF Radar images.

70 Data Treatment and Model Input Preparation5.4 Temperature and SalinityWater temperature and salinity are fundamental values if the aim is to re-produ e the oastal urrents due to thermohaline gradients.During the sear h of the best database that ts the oastal modeling needs,two problems had to be solved: no measurements from ruises or transe t ould be used be ause they did not over the whole basin. On the otherhand, many models provide temperature and salinity data over the wholeMediterranean Sea but with low resolution.The temperature and salinity 3D matri es adopted as initial ondition arefrom MFStep (Mediterranean Fore asting System Toward EnvironmentalPredi tions) daily dataset. They are omputed by the OPA Model and theirhorizontal resolution is 1/16 of a degree2.This database is onsidered a good ompromise between spatial and tempo-ral overage and high resolution. On the other hand the models applied inMFStep introdu e approximations and they are for ed with limatologi alfor ings that not permiting to resolve a number of pro esses. Additionallythere is the awareness that, using these elds as initial and boundary ondi-tions, an error is introdu ed along the oast also be ause the model resolution annot over up to the real oastline but only up to some kilometers oshore.Therefore a linear extrapolation is the proposed solution, adding, along the oast, the thermohaline information oming from rivers.In the 3D simulation also the river dis harge has to be imposed in the NorthAdriati Littoral. The annual mean values provided by the Basin Authorityof Friuli Venezia Giulia have been imposed as river open boundaries for ings.Daily dis harge values are provided for the Po river, be ause this time steppermits to des ribe in a realisti way the high variable hanges that o urseasonally and that strongly inuen e the dynami s of the Northern Adriati Sea.

2www.bo.ingv.it/mfstep/WP8/modeldesopa.htm

Chapter 6Modeling Barotropi Pro essesThe given des ription of the ontext in whi h the pro esses study is done andthe denition of the main for ings needed to simulate them permit to do astep further, the numeri al reprodu tion. In this hapter and in the next, thesystem omplexity is fa ed starting from a 2D investigation onne ted withall the oastal and intera tion barotropi pro esses to rea h, then, a moregeneral physi al view, even exploring the water olumn and the baro lini ity.In this hapter the tidal urrents reprodu tion is the fo us and the watermass balan e between the Veni e Lagoon and the open sea is investigated,both in terms of tidal and residual signals.6.1 The 2D Simulation SetupAll simulations presented in this part are for the year 2002 and have been arried out using a time step of 300 se onds. This time step ould be a hieveddue to the un onditionally stable time integration s heme of the nite elementmodel. The bathymetri data interpolated on the Adriati Sea nite elementgrid (Fig. 6.1) are taken from the NOAA 1 minute resolution dataset. Allsimulations have been run with the same wind for ing of the year 2002 and thelateral boundary onditions at the Otranto strait for the water levels derivedfrom the harmoni onstants and the storm surge model. The open boundaryhas been hosen as a straight line a ross the Strait of Otranto (Fig. 6.2). Thisparameterization was suggested by the results obtained in a previous workby Cushman-Roisin and Naimie (2002) who applied with su ess a niteelement tidal model of the Adriati Sea. This seems a logi al hoi e for the

72 Modeling Barotropi Pro esses

Figure 6.1: Bathymetry and nite element grid of the Veni e Lagoon and theGulf of Veni e, a subset of the numeri al domain of the model.Adriati Sea being the Strait of Otranto the narrowest part of the whole basin.Furthermore, being the Otranto line far away from the study area (Veni eLagoon and northern Adriati oast), disturban es to the numeri al solutionfor the region of interest, indu ed by the arti ial imposition of boundary onditions, an be avoided. At ea h node of the Otranto open boundary,water level time series are imposed. They are obtained by adding a surgesignal oming from an operational storm surge model (Bajo et al., 2007) tothe astronomi al tide omputed from harmoni onstants. The ontributionof the fresh water input released inside the basin by the main Italian riversis not taken into a ount. Flow dis harge measurements at the Malamo oinlet register a ow rate of 10000 m3s−1 and all three inlets together may show

6.1 The 2D Simulation Setup 73

Figure 6.2: The numeri al domain of the Adriati Sea and the lo ation ofthe tide gauges onsidered during the alibration pro ess.ow rates as high as 24000 m3s−1. This numbers an be ompared with themain river in the Adriati Sea, the Po river, that shows an average dis hargerate of 1500 m3s−1 (Ga£i¢ et al., 2002). Even if the river run-o stronglyinuen es the baro lin ir ulation in the Adriati Sea, it is far from givingappre iable ontributions to the barotropi water ir ulation in the oastalarea in front of the Veni e Lagoon. In parti ular, onsidering the Po riverruno, the adve tive uxes and the water level gradient indu ed by the riverdis harge indu e a momentum ux over the water olumn whi h inuen esthe water ir ulation only lo ally. Simulations in Umgiesser and Bergamas o(1998) show how the jet reated by the Po rst deviates to North East butthen dee ts southward due to the onservation of potential vorti ity. Maps

74 Modeling Barotropi Pro essesshow how it does not inuen e the study area near the inlets of the Veni eLagoon. Therefore the inuen e of the barotropi ontribution of the Poriver runo on the sea-lagoon water ex hanges and lo al water ir ulation an be negle ted.The bottom boundary ondition enfor es quadrati fri tion based on barotropi (depth-averaged) velo ity a ording to the lassi al quadrati drag law. Inthis appli ation two formulations for the bottom fri tion oe ient cB havebeen onsidered. For the deeper areas of the domain (Adriati Sea) the o-e ient is imposed to be onstant with a value of 2.5·10−3. However, in theshallow parts (Veni e Lagoon) the Stri kler formula has been used where thefri tion parameter depends on the water depth. This approa h was suggestedby the appli ation of the model to the Veni e Lagoon alone (Umgiesser et al.,2004). Inside the lagoon, dierent Stri kler oe ient have been used to dis-tinguish the behavior of hannels, tidal ats and the rest and at the threeinlets slightly dierent values of this oe ient are used in inow and in out-ow onditions to parameterize the unresolved physi al pro esses su h as thelo al head loss due to sudden expansion of the out-owing water (Umgiesseret al., 2004).What on erns the wind drag oe ient cD, a onstant value of 2.5·10−3 hasbeen adopted. The lateral diusion parameter AH has been set to 0. Theinitial onditions for the water levels and the velo ities are zero in the wholebasin and a spin-up time of 30 days for all the simulations has been imposed(Cu o and Umgiesser, 2005). This time was enough to damp out all thenoise that was introdu ed through the initial onditions.6.2 Barotropi Simulation ResultsIn this se tion the model results are presented. First the model alibrationthrough harmoni onstants is des ribed and then the water levels are vali-dated. In the third se tion, the uxes through the lagoon inlets are omputedand ompared with the ADCP data. The fourth part analyzes the reprodu -tion of the total levels and uxes, onsidering both the astronomi al and themeteorologi al signals. Finally the fo us is the reprodu tion of strong windevents, onsidering the two major winds blowing in the Northern Adriati .The rst one, is the old Bora wind from NE, that hara terizes extremeevents generally o urring during winter time (Orli¢ et al., 1992). The se -ond one is the wet, warm Siro o wind, oming from SE largely present inautumn and mostly responsible for the ooding events of the ity of Veni e(Orli¢ et al., 1992).

6.2 Barotropi Simulation Results 756.2.1 Calibration of harmoni onstantsThe model has been alibrated to reprodu e the harmoni onstants of thetidal onstituents M2, S2, K1, N2, K2, O1 and P1 in the Adriati Sea and,more spe i ally, in the Gulf of Veni e. These tidal onstituents are knownfor Otranto from a 9 years long hourly water level time series re orded byAPAT at the Otranto station. They are representative for the tides of thewestern Italian border of the strait. In addition to the astronomi al signal,surge values, produ ed by a numeri al model applied to the whole Mediter-ranean Sea, are imposed at the Otranto open boundary (Bajo et al., 2007).This surge model is adopted by the Veni e Muni ipality, running opera-tionally to predi t the ooding in the ity.To determine the tidal onstituents for the eastern Albanian border, an ite-rative pro edure has been applied whi h an be s hemati ally explained asfollows. First the harmoni onstants of Albania are set to the same valuesas the ones for Otranto. A one year long time series is produ ed from these onstituents and the surge signal is added to these water levels. For everynode on the border a linear interpolation is arried out between the waterlevels at Otranto and Albania.With these water levels for the open boundary, a one year long (8760 hours)simulation is arried out. This period is needed be ause it is the ne essaryand su ient time to separate the K2 and S2 frequen ies in the harmoni analysis of results (Foreman, 1996).At the end of ea h alibration run the harmoni onstants are extra ted fromthe model for the station losest to the study area, Diga Sud Lido (Fig. 6.2),and ompared with the empiri al ones. The dieren es between modelledand observed harmoni onstants are then used in hanging the harmoni onstants imposed for the Albanian side of the open boundary. In parti ular,the proportion of observed and modelled amplitudes and the time lag for thephases is used to ompute new tidal onstituents for Albania. With thesenew values, a new set of boundary onditions is omputed for ea h node onthe open boundary as explained above and a new run is performed.The alibration is ended when the dieren e between the amplitude of thethree main measured and modeled harmoni onstants (M2, S2, K1) fallsbelow 3 % and the phase shift is less than 2 degrees at Diga Sud Lido. Torea h this result, around 20 iteration were needed. At this point a omparisonfor the other 10 stations in the Adriati Sea is performed to assure a realisti tidal behavior in the whole Adriati Sea and not only an ad ho solution forthe Veni e Lagoon.

76 Modeling Barotropi Pro esses6.2.2 Water level validationFirst a omparison between modeled and measured harmoni onstants atDiga Sud Lido station has been arried out. In Tab. 6.1 the set of harmoni onstants obtained at Diga Sud Lido from the model alibration and frommeasurements taken by ISMAR-CNR in the year 2002, is shown. In Tab. 6.2Table 6.1: Comparison between model results (m) and observations (o) ofthe amplitude H and phase g of the whole set of tidal data at Diga Sud Lidostation.Hm Ho gm goConstituent [ m [ m [deg [degM2 23.00 23.38 292.5 291.4S2 14.67 14.71 298.2 296.7N2 4.13 4.16 290.4 290.1K2 5.67 5.83 312.8 311.3K1 20.53 20.00 88.6 87.9O1 6.32 6.55 59.0 53.4P1 5.56 5.39 70.9 72.0the nal set of harmoni onstants of the open boundary (Otranto and Al-bania) is listed. In Tab. 6.3 and Tab. 6.4 the amplitudes and the phase lagsof the main semi-diurnal and diurnal tides (M2, S2 and K1) are omparedwith the observations along the oasts of the Adriati sea (see Fig. 6.2 forreferen e).The phase in the table is expressed with respe t to the meridian of CentralEurope, as onventionally applied in Polli (1960). As explained in Tomasin(2005) the harmoni onstants are subje t to the periodi al hanges in theorbits of the sun and moon and for this reason they slightly hange in time.The algorithm des ribed in Tomasin (2005) gives the opportunity to updatethe date shown in Polli (1960), annualizing them for the year 2002.As I ould expe t, the alibrated model reprodu es the SSE at Diga SudLido station with high a ura y. I do not show the omparison graph forLido Station be ause the results are quite obvious even on the basis of theharmoni onstants shown in Tab. 6.1: small dieren es with observed datafor the harmoni onstants in this station are registered, with dieren es

6.2 Barotropi Simulation Results 77Table 6.2: Open boundary ondition. Amplitude H and phase g of the maintidal onstituents for the western (Otranto, O) and eastern station (Albania,A) of the SSE imposed as for ing along the open boundary of Otranto.HO gO HA gAConstituent [ m [deg [ m [degM2 6.8 133.1 8.58 59.33S2 4.0 141.0 4.65 71.89N2 1.2 131.2 1.61 1.84K2 1.1 136.9 1.52 221.33K1 2.3 91.1 4.04 19.33O1 0.9 75.7 1.71 33.77P1 0.8 85.1 1.37 29.04of millimeters in amplitude and some degrees for the phases; the highestdieren e at Diga Sud Lido is less than ve degrees for the O1 omponentwhi h is one of the less important omponents of the ones taken into a ount.The area of interest for this appli ation is the Northern Adriati Sea, whi h islimited in the Southern part by the line onne ting Pesaro to Pula (Fig. 6.2).The stations lo ated in this area are Fal onera, Porto Corsini, Trieste, Rov-inj, Pesaro and Pula (Tab. 6.3). In the northern half of the basin the twosemi-diurnal omponents are well reprodu ed with an absolute dieren e inamplitude never higher that 2 m (Tab. 6.3). Following the North-East oastof the basin, amplitude dieren es are os illating slightly around zero. Thesetwo harmoni omponents are quite in phase with measurements, with dif-feren es never higher than -6.7 degrees. This value is rea hed in Fal onerastation. There is a 20 minutes delay in the modelled data for these ompo-nents. In the same stations the major diurnal omponent is well reprodu ed,with -1.93 m (-7 %) as the highest dieren e in Trieste. When onsideringwhat is the main aim of this work, the modeling of the intera tion betweenthe Veni e Lagoon and the open sea, these results an be onsidered satisfa -tory. For the other stations in the Adriati Sea, the result for An ona stationis striking. Near An ona the M2 amphidromi point is lo ated. This meansthat tidal variation are small and water level measurements an be ae tedby higher errors be ause of the low signal to noise level. This ould explainthe high dieren e in phase (around -12 degrees). Going South, a general

78 Modeling Barotropi Pro essesTable 6.3: Comparison between model results (m) and observations (o) ofthe amplitude H and phase g of the most energeti tidal onstituents (M2,S2 and K1) at the tidal stations in the northern part of the Adriati Sea.

Hm Ho Hm - Ho (Hm -Ho)/Ho

gm go gm-goSite [ m [ m [ m [% [deg [deg [degLido M2 23.30 23.38 -0.08 -0.3 286.2 285.1 0.6S2 14.67 14.71 -0.04 -0.3 298.1 296.7 1.4K1 20.53 20.00 0.53 2.6 78.5 77.8 0.7Porto M2 16.54 15.50 1.04 6.7 301.2 305.10 -3.9Corsini S2 10.31 9.2 1.11 12.1 306.9 310.0 -3.1K1 18.89 16.5 2.39 14.5 92.5 89.3 3.2Fal onera M2 23.01 23.8 -0.79 -3.3 285.0 291.1 -6.1S2 14.80 14.10 0.70 5.0 290.3 297 -6.7K1 20.49 19.0 1.49 7.84 85.4 87.3 -1.9Trieste M2 24.47 26.4 -1.93 -7.31 280.9 278.1 2.8S2 15.84 16.00 -0.16 -1.0 286.1 284.0 2.1K1 20.81 19.3 1.51 7.82 83.4 78.3 5.1Rovinj M2 17.94 19.10 -1.16 -6.1 272.7 272.1 0.6S2 11.38 11.2 0.18 1.6 277.2 277.0 0.2K1 19.13 16.7 2.43 14.55 80.2 79.3 0.9Pula M2 14.82 15.0 -0.18 -1.2 266.1 267.1 -1.0S2 9.28 8.7 0.58 6.7 269.9 273.0 -3.1K1 18.19 16.1 2.09 12.98 78.4 77.3 1.1

6.2 Barotropi Simulation Results 79Table 6.4: Comparison between model results (m) and observations (o) ofthe amplitude H and phase g of the most energeti tidal onstituents (M2,S2 and K1) at the tidal stations in the southern part of the Adriati Sea.

Hm Ho Hm - Ho (Hm -Ho)/Ho

gm go gm-goSite [ m [ m [ m [% [deg [deg [degPesaro M2 11.23 12.7 -1.47 -11.57 310.5 313.1 -2.6S2 6.77 6.8 -0.03 -0.4 316.9 313.0 3.9K1 17.34 16.0 1.34 8.38 95.3 92.3 3.0An ona M2 6.15 6.5 -0.35 -5.38 324.0 334.1 -10.1S2 3.46 3.5 -0.04 -1.1 333.9 347.0 -13.1K1 15.59 13.7 1.89 13.80 96.3 96.3 0.0Sebenik M2 6.16 6.2 -0.04 -0.65 138.9 137.1 1.8S2 4.46 4.4 0.06 1.4 138.7 132.0 6.7K1 11.48 9.7 1.78 18.35 70.9 65.3 5.6Vieste M2 8.71 9.3 -0.59 -6.34 103.8 107.1 -3.3S2 5.81 6.0 -0.19 -3.2 110.0 115.0 -5.0K1 6.92 5.3 1.62 30.57 102.8 99.3 3.5Megline M2 9.440 9.0 0.44 4.88 108.3 101.1 7.2S2 6.16 5.9 0.26 4.4 112 103.0 9.0K1 6.85 5.2 1.65 31.73 73.8 60.3 13.5

80 Modeling Barotropi Pro essesoverestimation of the diurnal omponent K1 an be observed but it has tobe mentioned that the dieren e never ex eeds 1.5 m, even if this translatesinto a high error in terms of per entage (Fig. 6.3, middle panel, Tab. 6.4).The relatively high amplitude errors for K1 in the stations of the Dalmatian oast should be stressed. This might be due to the grid resolution along the oast. Be ause of the interest in simulating the North Adriati oastal dy-nami s, the applied nite element grid has high resolution in proximity of theVeni e Lagoon. The Dalmatian oast is less resolved than the Northern partof the Adriati Sea, be ause of the attempt to limit the number of elementsof the grid and to lower the time of omputation.For the other two omponents, M2 and S2, no general trends in amplitudedieren e an be observed. Phase dieren es do os illate around zero for allthe stations along the Adriati Sea, in reasing in module approa hing thesouthern open boundary at the Otranto Strait (Fig. 6.3, lower panel). Asmooth anti ipation of the real signal along the low resolved eastern oast ofthe southern Adriati and a spe ular delay along the western littoral, nearVieste station (Fig. 6.2), is observed for these harmoni onstituents. Thepresen e of the open boundary, where water levels are imposed, is ertainlyinuen ing the results for the stations lo ated lose to it.In on lusion, the hoi e of moving the open boundary to the Otranto straitwas orre t. In the southern part of the basin, errors are higher, mostly dueto the inuen e of the open boundary. On the other hand results in theNorthern part of the basin do not eviden e an inuen e of these modeling hoi es. What on erns the model results of the propagation of the tideinside the Veni e Lagoon I always refer to Umgiesser et al. (2004) for a morea urate des ription.6.2.3 Flux data validationOn e the model had been alibrated and validated with the water levels, ithas been used to estimate the water ex hange through the three inlets. Thepresen e of both tidal and meteorologi al data for ings has to be stressedbe ause the simulation of barotropi urrents in the Adriati Sea needs to onsider the whole set of signi ant for ings. From the eviden e of measure-ments at the inlets it an be dedu ed that the ow a eleration is generatedby the pressure gradient due to the sea-level slope. Velo ities are of the orderof 1 m/s and the bottom fri tion term is balan ed by the lo al a elerationand the horizontal pressure gradient (Ga£i¢ et al., 2004). The wind a tion ismainly barotropi at the inlets (Ga£i¢ et al., 2002). The onjun tion of tidal

6.2 Barotropi Simulation Results 81

Figure 6.3: Graph of amplitude, relative amplitude and phase dieren es ofthe three main modeled and measured harmoni onstants (M2, S2, K1) forthe ten stations in the Adriati Sea.

82 Modeling Barotropi Pro esses y les and atmospheri pressure and wind produ es extreme events propa-gating into the lagoon from the inlets, in parti ular when SE wind (Siro o)is blowing in a low pressure onguration (generally in winter time) (Ga£i¢et al., 2004).To validate the model results, only the tidal signal of the measured dis hargedata has been onsidered. Harmoni analysis is therefore applied to theADCP data olle ted at Lido and Malamo o inlets for the year 2002, ashas been done before for the water levels. The ontribution of the threemajor diurnal and semi-diurnal tidal omponents to the total ow rate - M2,S2 and K1 - is obtained and the parameters related to these onstituentsare presented in Tab. 6.5. As it an be seen from graphs in Fig. 6.4 thetwo signals mat h ni ely. To quantify the error a omparison between the omputed ux amplitudes and phases has been done in Tab. 6.5.Table 6.5: Water dis harge of the Lido and Malamo o inlet. Comparisonbetween empiri al data (o) (derived from ADCP measurements) and modelresults (m) of the amplitude A and phase g of the most energeti diurnal andsemi-diurnal frequen ies (M2, S2 and K1).Am Ao Am−Ao (Am −

Ao)/Ao

gm go gm −goInlet [m3/s [m3/s [m3/s [% [deg [deg [degLido M2 4400.1 4366.8 33.28 0.76 254.9 244.8 10.1S2 2596.3 2504.8 91.5 3.65 267.2 255.4 11.8K1 1895.8 1790.4 105.4 5.9 21.3 14.4 6.8Malamo o M2 4725.2 4682.0 43.2 0.92 245.5 232.1 13.4S2 2825.0 2790.7 34.3 1.23 258.4 243.1 15.3K1 1892.1 1717.4 174.7 10.2 13.2 4.0 9.2Analyzing the tidal reprodu tion of water uxes, dierent onsiderations anbe done for diurnal and semi-diurnal omponents. Satisfa tory results areobtained in simulating the M2 and S2 omponents: the amplitude error isalways less than 3.65 % for both inlets (Fig. 6.4, Tab. 6.5). The M2 andS2 modelled uxes anti ipate the measured ones by around 20 minutes atLido Inlet and 30 minutes at Malamo o Inlet. The worst reprodu tion, asin the ase of water levels, is again for the K1 onstituent. Following theresults of the harmoni analysis, from ADCP data it an be stated that M2,

6.2Barotropi SimulationResults83

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Figure6.4:Tidaldis hargetimeseries omparisonbetweenmodeledandmeasureddatainLidoandMalamo oinlet.

84 Modeling Barotropi Pro essesS2 and K1 omponents represent about 50 %, 30 % and 20 % of tidal signal(Tab. 6.6). Weighting ea h omponent with these values the omprehensivetidal dieren e in amplitude is 2.7 % for Lido inlet and 2.9 % for Malamo oinlet. The phase anti ipation of modelled tidal uxes is 23 minutes for Lidoand 30 minutes for Malamo o. Moving from harmoni onstituents to themodelled and observed tidal time series, the omputed orrelation oe ientis 0.99 both for Lido and Malamo o inlets. Moreover, the model reprodu esTable 6.6: Weighted dieren es of dis harges in amplitude (A) and phase(g)(in terms of minutes) for Lido and Malamo o inlets.Inlet Per of modelled A[%] g[minTidal Fluxes [%Lido M2 49.5S2 29.2 2.7 23K1 21.3Malamo o M2 50S2 30 2.9 30K1 20an additional aspe t, already seen in measurements (Ga£i¢ et al., 2002). Theobserved semi-diurnal signal at the Malamo o inlet anti ipates the Lido oneby about half an hour (Ga£i¢ et al., 2002). The simulated phase lag is ofabout 20 minutes, ni ely mat hed, even if slightly underestimated.The ux modeling is stri tly onne ted with two fa tors: the apability inreprodu ing the dynami s in the lagoon and the parameterization of thebottom stress inside the three onne tion hannels. The bottom fri tion oe ients hosen during the alibration phase are spe i for ea h inletwith dierent values applied to simulate the inow and outow dynami s.The nal values hosen are the ones that more uniformly distribute the erroron all three inlets and reprodu e the intera tion pro esses.To explain the dieren es with the empiri al data I an distinguish two dier-ent groups of errors: one related to the measured data and one related to thenumeri al model. The empiri al dis harge data, as explained in se tion 2.3,have been obtained from the verti ally averaged water velo ity value mea-sured by ADCP probe for one xed lo ation inside ea h inlet. From Ga£i¢et al. (2002) I know (table 1) that the ADCP velo ity data are ae ted by

6.2 Barotropi Simulation Results 85an error of around 5 % for the M2 and 10 % for the K1. Sin e the dis hargedata is omputed from the velo ity data by applying a regression formula,the errors given above are ertainly a lower bound for the errors of the uxdata.A further sour e of error for the empiri al data is related to the harmoni analysis. In fa t, due to the high residual signal generated by intense meteo-rologi al events, the amplitude and the phase values obtained for ea h maintidal onstituents from the harmoni analysis are subje t to high relativeerrors.What on erns the model, a sour e of error an be related to the reprodu tionof the SSE outside and inside the inlets. The dis harge rate through the inletis dependent on the SSE gradient along the inlet hannel and therefore thea ura y of the SSE inside and outside the lagoon strongly ae ts the modelresults. The in rease in resolution for what on erns the lagoon, des ribing ina more realisti way shallow areas and hannels, in terms of internal dynami sand bottom fri tion, an improve the internal reprodu tion of SSE. Finally,as mentioned in Ferla et al. (2007), the harmoni onstants measured inthe lagoon have hanged signi antly during the last de ades be ause ofthe morphologi al hanges. It is realisti to suppose that the use of newbathymetri data to reprodu e the morphology ould redu e the error ofthe model for the SSE and onsequently also the dis harge rate through theinlets.6.2.4 Residual Levels and FluxesAn analysis on the reprodu ed uxes with respe t to the meteorologi al im-pa t on hydrodynami s has also been arried out. In Fig. 6.5 the Fast FourierTransform (FFT) graph for the residual signal, al ulated subtra ting thetides from water level at the Lido inlet, is presented. For this nal part theForeman harmoni onstant analysis has been applied to produ e the residualwater level time series (Foreman, 1978). An interesting aspe t is the presen eof two peaks, related to the 11 hours and 22 hours periodi al signals. Theseare the two main sei hes of the Adriati Sea (Tomasin and Pirazzoli, 1999)and the model is able to reprodu e them, better the 22 hours sei he thanthe 11 hours one. Comparing model and real data signals, it an be notedthat the model, even if it is able to reprodu e the 11 hours sei he, presents adispla ement in frequen y, with a shift to higher frequen y values (Fig. 6.5).Applying the same kind of analysis to the residual uxes for Lido and Malam-

86ModelingBarotropi Pro esses

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Figure6.5:FastFourierTransformofresidual omponentsoflevelsintheLidoinlet.

6.2Barotropi SimulationResults87

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Figure6.6:FastFourierTransformofresidual omponentofuxesintheLidoandMalamo oinlets.

88 Modeling Barotropi Pro esseso o on e more the two sei hes are registered by the model (Fig. 6.6) whi hare even more evident. It seems that some semi-diurnal omponents still re-main in the residual signals, perhaps the overtide portion of sea breeze. Themodel does not reprodu e them but this an be explained by the meteorolo-gi al for ing that was applied oming from ECMWF model data. These datahave a frequen y of 6 hours and it is ertainly not possible, with this oarsetemporal and spatial resolution of 0.5 degrees, to produ e a signal of limitedspa e and time extension like the sea breeze. Additionally it has to be saidthat the meteorologi al data time step, 6 hours, ould introdu e some arti- ial frequen ies in the model results and that ould explain the peak around3.2E-4 Hz in the model data. These results ould be interfa ed with otherstudies done on residual urrents at the Veni e Lagoon inlets from ADCPdata (Ga£i¢ et al., 2004). In Ga£i¢ et al. (2004) the sei hes signals an beisolated and the obtained information is omparable with the one from ourstudy, even if the analysis has been done on axial velo ities and not on uxesas done here.Considering the whole modeled uxes for Lido and Malamo o inlet it anbe noted that the tidal signal ontained is 95 % of the total varian e forLido inlet and 97 % for Malamo o inlet, values omparable with the onesobtained by measurements (Ga£i¢ et al., 2004). From Fig. 6.6 it an be seenthat the residual variability is due to the meteorologi al for ings.6.2.5 Extreme wind eventsThe whole simulated period has been analyzed and a parti ular portion, fromthe 20th of November to the end of De ember, has been onsidered. Thisperiod shows the two main extreme events of the year, with a strong Siro owind blowing around the 24th of November and a long Bora event lastingseveral days before the 8th of De ember. In Fig. 6.7 the wind data measuredby the O eanographi Platform CNR for the hosen period are shown, bothspeed and dire tion.The Pearson orrelation oe ient has been omputed, rst on the omplete hosen time window, and then on the two singular extreme wind events. Theinterval of onden e hosen is 5 %. High orrelation is registered for uxes,0.89 for the total temporal range, 0.96 for the Bora event and 0.89 for theSiro o event. In the three ases the p-value is nearly 0.On the other hand the orrelation of water levels is higher for the two singlewind events, 0.9 for Siro o and 0.94 for Bora, ompared with the orrelationof the whole time series, 0.82. This ould be as ribed to the hoi e of imposing

6.2Barotropi SimulationResults89

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Figure6.7:Winddata(dire tionandspeed)forasigni antextremeeventperiodofDe ember2002.

90 Modeling Barotropi Pro essesmodeled storm surge for ings at the open boundary instead of measured ones.In fa t it has to be mentioned that storm surge modeling is a di ult taskbe ause of the strong dependen e on the hoi e of meteorologi al for ings.Anyway, it an be stressed that the orrelation omputed here is omparablewith the one in Bajo et al. (2007).Be ause the sub-sample for the Siro o wind event onsists only of around 30values, it has been de ided to ompute also the Kendall's Tau, better suitedfor small samples. The Kendall's Tau gives a value of 0.74 for the water levels(p-value 2.2E-9), and 0.84 for the uxes (p-value 1.266E-14). These valuesprove a good orrelation even on this short wind event.It is interesting to note that total uxes seem to be reprodu ed better thantotal water levels (Fig. 6.8). This an be explained be ause uxes at theinlets are mainly tidally driven (Ga£i¢ et al., 2004) and, as shown, the tidalsignal is better reprodu ed than the residual one. As an example Fig. 6.8shows the omparison between the measured and the modeled total waterlevels and uxes time series, stressing learly the good mat h.Some dieren es in extreme event reprodu tion an be also onne ted withthe rough resolution of ECMWF data, 1/2 of a degree, whi h does not re-produ e adequately the wind variability in the study area. A previous work ompared results from the SHYFEM model, in its operational version, for edwith dierent wind elds, the ECMWF ones des ribed above and the Limi-ted Area Model (LAMI) wind elds (Zampato et al., 2007). The latter oneprodu ed more intense wind elds and was apable of resolving the meso-s ale features of the wind in the study area with a higher orrelation withmeasured data (Zampato et al., 2007). Unfortunately, LAMI wind elds werenot available for the onsidered period.

6.2Barotropi SimulationResults91

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Figure6.8:Comparisonbetweenresiduallevelsanduxesmodeledandmea-suredinLidoinlet.

92 Modeling Barotropi Pro esses

Chapter 7Modeling Baro lini Pro esses7.1 The 3D Simulation SetupTwo dierent sets of simulations have been arried out to study the 3D hy-drodynami pro esses in the area. The rst is onne ted with the appli ationof idealized for ings over the realisti basin and the study of its response, these ond deals with realisti for ings where the baro lini pressure gradientterms and the adve tion terms are onsidered or negle ted.7.1.1 Idealized For ing SimulationsThree simulations have been performed over the Adriati Sea-Veni e Lagoonbasin. The rst simulation introdu es an idealized tidal signal at the openboundary at the Otranto strait: a sinuisoidal 12 hours period, amplitude 40 m, tidal timeseries is hosen. This hoi e is driven by the fa t that this ouldbe a realisti approximation of the M2 tide in the Adriati Sea, whi h is oneof the most energeti tidal signals in the northern part of the basin (Polli,1960; Bellaore et al., 2008). Constant values of temperature (14 degrees)and salinity (35 psu) are imposed over the whole basin as initial onditions.Idealized river dis harges are given, with freshwater owing into the sea atthe same temperature of the basin. The amount of dis harge is taken fromaverage annual means. The simulation period is 16 days, be ause 15 daysare onsidered a suitable period for the spin up. The 16th day is analized.The se ond two simulations introdu e idealized wind elds: a persistent Boraevent, dire tion from NE and wind speed 14 ms−1, whi h is a realisti value

94 Modeling Baro lini Pro esses onsidering measures; and a persistent Siro o event, dire tion from SE, wind12 ms−1. No tidal for ing is introdu ed and river dis harges are set as in theprevious simulation. As initial onditions, temperature, salinity, velo ity andwater level elds from a 15 day simulation of real onditions of January 2004have been used. These initial onditions are representative of a typi al wintersituation in the North Adriati with the presen e of the oastal urrent. Afterthis, three days of wind events are simulated and the last day is averagedand analyzed.7.1.2 Sensitivity SimulationsThe se ond set of simulations deals with realisti for ings during year 2004.The hoi e is onne ted with the availability of HF Radar measurements forthe same year, that will be ompared with model results in the next se tion.The wind elds are taken from T511 ECMWF (European Centre for MediumWeather Fore ast) 0.5x0.5 degrees, 6 hour data. The temperature and sa-linity 3D matri es adopted as initial ondition are from MFStep (Mediter-ranean Fore asting System Toward Environmental Predi tions) daily dataset.Their horizontal resolution is 1/16 of a degree. A realisti water level tidalsignal is imposed at the open boundary at the Otranto Strait applying thepro edure des ribed in Bellaore et al. (2008) and obtained by real harmoni onstants for the Otranto Strait in the year 2004. The seven major harmoni onstants in the Adriati Sea are imposed and the surge signal, produ ed bya surge model running over the whole Mediterranean Sea (Bajo et al., 2007),is added to the tidal water level timeseries at the open boundary. The monthof May is simulated and the monthly average is analized. This average ltersout the main inuen e of tides, being the most energeti tidal signals in thisarea the omponents M2, S2, K1. Three simulations have been performed:the rst uses the omplete terms of the primitive equations (run A), the se -ond negle ts the baro lini pressure gradient terms (run B) and the thirdnegle ts also the adve tion terms (run C).7.1.3 Realisti Simulation of the year 2004A omplete simulation for the year 2004 has been performed. All the for- ings des ribed in the previous se tion have been imposed. The results ofthis simulation are used to provide information about the dierent vorti itypatterns in three dierent periods of the year (February, May, November) tostress the response to for ings that ould produ e spe i horizontal and ver-

7.2 Baro lini Simulation Results 95ti al stru tures (vorti es, verti al strati ation). Monthly averaged surfa e urrents maps are provided, omparing model results with HF Radar Data.The se ond kind of analysis is done to dene the persistent surfa e stru tures onne ted with the a tion of dierent winds (Bora Events, Siro o Events,other wind events, alm Events). Detided velo ity elds are onsidered toeliminate the tidal ee ts. Even in this ase a omparison with HF Radardata is provided.7.2 Baro lini Simulation ResultsOne of the variables that an easily give an overview of the dynami of thestudy area is vorti ity and in the following se tions, averaged vorti ity mapswill be investigated to add information about persistent small s ale pro esses.The investigation is arried out in the surfa e layer and in the se ond layer,between 2 m and 4 m.7.2.1 Idealized for ing impa tThe simulations using idealized for ings are here dis ussed. The rst simula-tion (Fig. 7.1) is shown as 12 hours average over the 16th day of simulationunder the only for ing of a 12 hours tidal signal. The hoi e to onsiderthe average value is onne ted with the fa t that the interest is not fo usedon tidal urrents, already investigated in the previous hapter, but on tidalindu ed urrents (se ondary ee ts). In fa t, what is seen is the presen e ofpositive (to the North) and negative (to the South) vorti ity poles, in orre-spondan e with ea h layer. This is not onne ted with the main tidal signalbut with a residual persistent signal. The same pattern is mantained evenon the se ond layer, onrming a barotropi behaviour of tidal urrents nearthe inlets. A rst result that emerges from this eviden e is that the a tionof tides, even if modelled in 3D, are barotropi in this oastal intera tionarea, in their primary and se ondary signals. It has to be mentioned thatthe vorti ity values presented in these maps are ontained in a small range[-2E-5,+2E-5 due to the fo us on the se ondary ir ulation aused by tides.From Fig. 7.2 it an be seen how dierent winds hange abruptly the surfa epattern of vorti ity: Bora Wind denes a large strip of oastal negativevorti ity. This result has to be interpreted onsidering the fa t that theinitial ondition of the simulation is realisti , that means that the wind a tson a urrent pattern in whi h the general geostrophi urrent an be seen

96 Modeling Baro lini Pro esses

Figure 7.1: Vorti ity maps of the surfa e and se ond layer for the idealizedsemidiurnal tide simulations. A 12 hours average is applied to eliminate thetidal impa t.

Figure 7.2: Vorti ity maps of the surfa e and se ond layer for the idealizedBora wind simulations, averaged over the 3rd day of simulation.

7.2 Baro lini Simulation Results 97

Figure 7.3: Vorti ity maps of the surfa e and se ond layer for the idealizedS iro o wind simulations, averaged over the 3rd day of simulation.along the littoral. The water, as an average, ontinues to ow from Northto South. A map of negative oastal vorti ity should be interpreted as theeviden e of a de rease in urrents from oshore to the littoral. The oastal urrents tend to ow parallel to the oast following the isobaths, de reasingin intensity along the 2 km littoral strip during wind events and seem not tobe ee ted by the a tion of the inlets dynami s on the surfa e.The se ond layer (Fig. 7.2) shows a more dynami pattern, whi h is inter-preted as a weaker a tion of the wind and an in reased persisten e of typi alintera tion pro esses at the inlets. A tongue of more negative vorti ity isseen at the Malamo o and Chioggia Inlets (the entral and the southernones) that should be due to the outow oming from the Lagoon. In Cu oand Umgiesser (2006) it is shown how the Bora winds set up a ir ulation inthe Veni e Lagoon where water enters in the Lido inlet and outows from the entral and the southern ones, exa tly what an be seen in this simulation.It has to be mentioned on e again that, in this idealized simulation, no tidalinuen e is onsidered during the three days run.Fig. 7.3 shows the impa t of Siro o wind, whi h hanges strongly the surfa epattern. Considering also the surfa e urrent patterns (not shown here) thepositive vorti ity an be interpreted as a hange in urrent dire tion and asa displa ement of the more energeti oastal urrents. Siro o wind deta hesthe mean geostrophi oastal urrent oshore, keeping stronger urrents a ouple of km from the littoral. As Bora, it a ts mostly at the surfa e. Theinteresting aspe t is the la k of symmetry between the a tion of the two windson the se ond layer: the positive vorti ity, between Chioggia and Malamo o

98 Modeling Baro lini Pro essesinlets, is stronger than the one between Malamo o and Lido inlets. Thismeans that the Siro o wind a ts predominantly in the Southern end of theVenetian littoral. On the other hand the two areas between the inlets havequite a similar behaviour during Bora events, with a more homogeneousa tion of this wind on the whole area.The last onsideration is on the area of non-zero vorti ity in the three sim-ulations. The a tion of winds involves the whole basin, while the a tion oftides an be dete ted just in the near oastal area and in the proximity ofthe three inlets. This result is in agreement with what has been seen byKova£evi¢ et al. (2004), from HF Radar measurements. Data showed thatthe tidal inuen es is below 20% 4 km oshore, while is predominant in theinlets (Ga£i¢ et al., 2004).7.2.2 Sensitivity AnalysisFrom HF Radar measurements and analysis (Man ero Mosquera et al., 2007)vorti al sub-mesos ale stru ture are seen, when the wind is blowing weakly,in front of the littoral areas between the Veni e Lagoon inlets. Additionally,really lose to the littoral, where the HF Radar annot olle t measures,other small s ale vorti al re ir ulation stru tures are seen. In order to studythe pro esses that lead to the formation of these additional small velo itypatterns, three simulations are performed for the month of May 2004, apply-ing the realisti set of winds, tides and river runo. As des ribed in se tion7.1.2, we all the rst simulation, whi h uses the omplete terms of the prim-itive equations, run A, the se ond one, whi h negle ts the baro lini pressuregradient terms, run B and the third one, whi h negle ts even the adve tiveterms, run C.In Fig. 7.4 the surfa e and the se ond layer monthly averaged vorti ity eldsare shown, spe i ally for the area between Malamo o and Chioggia inlet.The monthly average eliminates the tidal signal, whi h is mainly dened bydiurnal and semi-diurnal signals, permitting the analysis of residual urrents.The maps of run A, show a ore of positive vorti ity along the littoral, thatpersists even in the se ond layer. Run B, whi h does not ompute baro lini pressure gradients, still maintains the positive ore but the values are weaker.This means that a small impa t of temperature and salinity gradients inu-en e the dynami s of this area. However they annot be onsidered thedriving pro esses keeping this vorti al persistent stru ture. Run C, in whi heven the adve tion terms are not omputed, gives a lear information: novorti al stru ture are dete ted in the area and even the two inverse vorti ity

7.2 Baro lini Simulation Results 99

Figure 7.4: Vorti ity maps of the surfa e and se ond layer for the threesensitivity runs: with all the terms omputed (A), negle ting the baro lini pressure gradient only (B), negle ting the baro lini pressure gradient andthe adve tion terms (C).

100 Modeling Baro lini Pro essespoles at the inlets disappear. It an be on luded that the physi s onne tedwith these vorti al phenomena are due to adve tion mainly. The positivevorti ity hara terizing these patterns, identify them as a kind of intera tionpro ess, stri tly onne ted with the inlet dynami s.7.2.3 Run of the year 2004All the following maps (the monthly averaged vorti ity and total surfa e ur-rent maps and the detided surfa e urrents maps) are referred to the year2004. Pro esses onne ted with seasonal patterns are investigated, followingthe approa h proposed in Man ero Mosquera et al. (2007). For the analysisof wind a tion the data have been divided in subsamples. The wind mea-surements in the CNR Platform (Fig. 3.1) are used to divide the wind eventsinto four ategories: alm events (wind speed under 3 m/s), Bora winds(dire tions in the range 202.5-247.5 degrees Azimuth, from North-East) andSiro o winds (dire tions in the range 297.5-342.5 degrees Azimuth, fromSouth-East) (Man ero Mosquera et al., 2007). Other wind events are theones not in luded into these three ategories. Some pro esses have alreadybeen dete ted by HF Radar and these measurements are used here to validatethe model results.Monthly Averaged Surfa e Current PatternsIn Fig. 7.5 the surfa e and se ond layer vorti ity pattern for February 2004 isshown. To interpret this eld the surfa e urrent eld presented in Fig. 7.6 isne essary. A mean urrent owing to the South is dete ted and the oupledpole of positive and negative vorti ity near the inlets an be interpreted asthe enhan ement of its meandering shape, approa hing the oast North ofthe entral inlet and then deviating oshore in the proximity of it. The mean urrent is reprodu ed by the model even if the ee t of the inlets mean outowis stronger than measures. In fa t the higher dire tion errors are mostly loseto the inlets and to the borders of the omparison area, where the HF Radarmeasures dire tion with an in reased error due to the existen e of the blindarea, already explained. Comparing the rst and the se ond layer of Februaryvorti ity maps, the same patterns are seen, omrming that a well mixed,barotropi verti al stru ture persists for this month, in agreement with thegeneral information about the Northern Adriati (Fran o et al., 1982).May 2004 has a ompletely dierent urrent pattern, showing a urrent re-versal. The interesting thing is that surfa e vorti ity maps are quite similar

7.2 Baro lini Simulation Results 101

Figure 7.5: Monthly averaged vorti ity maps of the surfa e and the se ondlayer for months February (A), May (B), July (C) and November (D), refer-ring to the year 2 004.

102 Modeling Baro lini Pro essesto the ones of February (Fig. 7.5) but the mean urrent shows a meanderingow from South to North. The reason an be found in the presen e of manySiro o Events in this month. Also in this ase the mean ow is reprodu edby the model, even if the HF Radar data show higher variabilities in themeanders. As for February the higher dire tional errors are registered in thesouthern end of the area (Fig. 7.6). Generally, in the area in front of the entral inlet there is a small underestimation of measured surfa e urrentspeed (-0.05 m/s).The month of July 2004 presents more persistent vorti al stru tures, whi hare well reprodu ed by the model (Fig. 7.7). This patterns ould be seenbe ause of weaker wind events in that month (speed less than 6 m/s). Asin the previous ases the higher dire tion errors are registered at the border.The surfa e and se ond layer vorti ity patterns for this month diers morethan the previous ases and this eviden es the evolution of a verti al stru turethat is weakened by depth (Fig. 7.5).November 2004, whi h is hara terized by strong Bora events, shows analigned surfa e urrent pattern from North to South, well mat hed by themodel. This is the month best reprodu ed in dire tion by the model. Itseems that the model is better reprodu ing periods of small variability inwind dire tion. In fa t, the wind for ing is from ECMWF dataset, with ahorizontal resolution of 0.5 degrees, not enough to des ribe all the small s alewind variations.For the four months an additional aspe t is seen, onne ted with the riverdynami s. Along the oast a strip of negative vorti ity is seen, whi h isenhan ed in July and November. In orresponden e with the main rivers,poles of positive vorti ity are present: it seems that there is a deviation tothe North near the river mouth and then a deviation to the South goingoshore, as an ee t of potential vorti ity onservation.Response to wind events - Comparison with HF Radar DataThe omplete dataset of year 2004 (from February to De ember) has beenanalyzed produ ing, both for model and for measurements, four sub-samples orresponding to detided surfa e urrents during Bora, Siro o, alm andother winds events. In Fig. 7.8 the Bora pattern an be analyzed: there isa good mat h between model and measurements and the main ee t of thewind is the enhan ing of the oastal urrents in the southern dire tion. Thestrength of the wind tends to eliminate the ee ts of the three inlets aligningthe urrent to the littoral. The Bora wind ee t in dire tion is reprodu edwith errors not higher than 20 degrees in most of the area. Higher errors

7.2 Baro lini Simulation Results 103

Figure 7.6: Monthly averaged maps of HF Radar (green) and Model (red)surfa e urrents (left panel) for months February (A) and May (B) 2004. Di-re tion errors [degrees and speed errors [m/s maps are shown in the entraland right panels.

104 Modeling Baro lini Pro esses

Figure 7.7: Monthly averaged maps of HF Radar (green) and Model (red)surfa e urrents (left panel) for months July (A) and November (B). Dire tionerrors [degrees and speed errors [m/s maps are shown in the entral and rightpanels.

7.2 Baro lini Simulation Results 105are seen, on e more, at the southern border. The Siro o wind produ esa ounter urrent from South to North intera ting with the se ondary inletdynami s. The dynami is the same as in the idealized simulations, onrm-ing the predominant a tion of the wind even when all the other for ings areintrodu ed. Fig. 7.9 shows two vorti al stru tures South of the Lido and theMalamo o inlets both for alm and other wind events. During alm windevents the sub-mesos ale stru tures are maintained by the tide and the in-uen e of the inlets is predominant. This emerges also from the sensitivityanalysis done in se tion 7.2.2, that onne ts this kind of pro esses to theadve tive a tion of inlet tidal y les.The error in dire tion are quite high for Siro o, alm and other wind events,while Bora is well reprodu ed. On e more the reason an be onne ted withthe di ulty of the model to simulate lo al variable wind events with thelow resolution wind for ing dataset hosen.

106 Modeling Baro lini Pro esses

Figure 7.8: Map of averaged detided surfa e urrents for the Bora (A) andSiro o (B) wind events - omparison between measured HF Radar data(green) and modelled data (red). Dire tion errors [degrees and speed errors[m/s maps are shown in the entral and right panels.

7.2 Baro lini Simulation Results 107

Figure 7.9: Map of averaged detided surfa e urrents for alm (A) and otherwind (B) events - omparison between measured HF Radar data (green) andmodelled data (red). Dire tion errors [degrees and speed errors [m/s mapsare shown in the entral and right panels.

108 Modeling Baro lini Pro esses

Chapter 8Summary and Con lusionsIn this work the main aim was to reprodu e by numeri al modeling some ofthe most important hydrodynami patterns o urring along the oast of theNorthern Adriati Sea and to study the intera tion pro esses between theVeni e Lagoon and the open sea.Untill now, no major studies have been arried out that try to model the ex- hange me hanisms through the Veni e Lagoon inlets. It is also the rst workin this area that tries to model the intera tion dynami s, running togethera model for the lagoon and the Adriati Sea. The in reased spatial resolu-tion a hieved in the inlets area permits a realisti study of the intera tionpro esses.A ertain eort has been made in the denition of the state of the art ofhydrodynami modeling in the Adriati Sea, whi h is a preferable basin forthe pro esses investigation be ause of its morphologi al hara teristi s andof the main for ings. This overview led to the hoi e of the most suitabletool for the oastal modeling, identied in the SHYFEM Model.The need of high spatial resolution and realisti datasets as for ings is stressed,be ause they strongly impa t on the quality of modeling results. Additio-nally, also the model numeri al hara teristi s have been studied and testedto ertify its apability to reprodu e the kind of small s ale pro esses whi hhave been investigated in this work.However, the ore of this PhD Thesis has been the numeri al modeling ofspe i pro esses and temporal ranges and the approa h was to pro eed fromlower to higher omplexity in the study. The rst simulations have beenperformed in 2D, limiting the study to barotropi pro esses to reprodu e thedis harge rate through the lagoon inlets driven by the a tion of the tide and

110 Summary and Con lusionswind (Ga£i¢ et al., 2002).The spatial resolution of the model varied from 30 m inside the Veni e Lagooninlets to 30 km in the middle of the Adriati Sea, with a transition zone lose to the lagoon inlets, hara terized by a resolution of 300 m. The openboundary has been hosen as a straight line a ross the Strait of Otranto onwhi h the tidal SSE is imposed. The model has been alibrated to reprodu ethe tidal propagation in the Adriati Sea and in the Veni e Lagoon. The SSEalong the eastern end of the open boundary line of Otranto and the bottomfri tion oe ient inside the Veni e Lagoon basin were hanged during the alibration. For the validation the model results have been ompared tomeasured data of harmoni onstants olle ted in stations lo ated along boththe western and the eastern oast of the Adriati Sea.For what on erns the tide, the model reprodu ed the set of harmoni on-stants for the Diga Sud Lido station for the most energeti tidal onstituents(M2, S2 and K1). The results obtained for the other stations lose to theVeni e Gulf, Fal onera, Trieste and Rovinj, were in good agreement with theempiri al data. The SSE oshore the Veni e Lagoon has been in fa t repro-du ed with an error always lower than 2 m for the amplitude of the maintides and with a phase dieren e not higher than 10 degrees. These resultsare in a ordan e with the rst task of this work, whi h is the reprodu tionof the tidal ow through the three lagoon inlets.After this rst step, the water uxes through the inlets have been omputedby the model when tide and wind are for ing the basin. The results havebeen ompared with empiri al data of water dis harge derived from ADCPmeasurements olle ted inside ea h inlet. The model reprodu ed the uxesthrough the inlets with a good agreement for both of them and an averageoverestimation less than 2.9 % with a time anti ipation of about 20 minutes.The frequen y analysis ondu ted using the FFT both on residual signals oflevels and uxes stressed the apability of the model to reprodu e sei hesand their ee ts on the ir ulation in the intera tion areas. Free os illationswere orre tly reprodu ed.The SHYFEM Model has been already applied to the whole Mediterraneanbasin to fore ast water levels, fo using on the Venetian area (Bajo et al.,2007). The omparison between modeled and measured residual levels timeseries showed how the oupling of tidal and meteorologi al for ings, in ludingthe surge impa t, leads to a eptable results. The su ess of these simulationson the reprodu tion both of the SSE, inside and outside the Veni e Lagoon,and of the tidal ow, through the lagoon inlets, indi ates that the niteelement model is performing adequately on the barotropi mode. For therst time the physi al pro esses that drive the intera tion between the two

111basins were reprodu ed, as the ux modeling shows. Clearly, the good resultsreprodu ing dis harges through the inlets are due to the fa t that the lagoonis modeled together with the Adriati Sea. Without the lagoon, the waterlevels ould be ertainly reprodu ed, but not the uxes between the sea andthe lagoon.The se ond task of this work was the reprodu tion of baro lini pro esses.3D runs were required to introdu e and study the ee ts of freshwater, tem-perature and salinity horizontal gradients and the a tion of turbulen e.Additionally, the simulations performed introdu ing ideal for ings, tides andthe Bora and Siro o winds, led to a better understanding about the a tionof ea h of them on the study area, both on the horizontal and verti al s ale.The se undary ee ts of tides, shown in the averaged maps of the surfa eand the se ond layer, were seen, dening their barotropi a tion mainly nearthe inlets. The tidal signal is less that the 20% some kilometers oshore asalso seen by measurements (Kova£evi¢ et al., 2004).What on erns results of the idealized winds runs, the Bora a ts along thelittoral enhan ing the geostrophi urrent and deta hing it oshore, parallelto the isobaths. On the other hand the Siro o auses a hange in the dire -tion of oastal urrents, from South to North. These 3D runs investigatedthe oastal verti al stru tures, dening the limit of wind a tion below thesurfa e.The sensitivity analysis was able to dene the predominant ee t of adve tionin the sub-mesos ale vorti al stru tures, whi h are present lose to the oastnear the three inlets of the lagoon. One of the main results of this work wasthe onrmation of the model apability to des ribe small s ale pro essesand the possibility to model the intera tion between the lagoon and theopen sea, be ause of the high resolution rea hed along the littoral. In thisway, the model was able to simulate the near oast pro esses that ould notbe studied with the HF Radar measurements.The analysis of dierent wind elds on the surfa e ir ulation dened themain horizontal urrent stru tures, learly identifying the pro esses on-ne ted with winds with low dire tional variability, su h as Bora.The model obtained also a general des ription of the oastal urrent be-haviour during the year 2004, showing the barotropi stru tures o urredduring February and the more omplex patterns seen in May, with persistentvorti al stru tures due to the presen e of many alm wind events.In the future, a new analysis, introdu ing higher resolved wind elds as modelfor ings, ould show higher pre ision in modeling these pro esses.The nite element approa h used in the SHYFEM Model, with its variable

112 Summary and Con lusionshorizontal resolution, showed to be a suitable tool for the investigation of oastal pro esses and its implementation in monitoring would be ome a pre- ious help for the oastal management in the future.

Appendix AThe Arakawa GridsThe problem of what kind of horizontal dis retization to apply in o ean mo-dels is quite old. From the overview presented in hapter 2 what an be seenis that many models apply one of the possible hoi es proposed by Arakawaand Lamb (1994). Dierently from what an be thought, arranging the omputation of all variables in the same grid point presents disadvantages,therefore new solutions are needed.Arakawa and Lamb (1994) presents ve type of grids, identied with lettersfrom A to E.A gridthe Arakawa A grid is the basi unstaggered grid, in whi h all the variablesare held in the same point Fig. A.1.

Figure A.1: Arakawa A grid

114 The Arakawa GridsB gridThe Arakawa B grid omputes the velo ity variables, zonal and meridional,in the same point and they are semi-staggered Fig. A.2. Usually this kindof grid permits an easier formulation of the Coriolis term and favours theimplementation of ba k-forward s heme, be ause of the same lo ation of thetwo velo ity omponents.Figure A.2: Arakawa B grid

C gridThe Arakawa C grid is a fully staggered grid where the two omponents of thevelo ity and the water levels are omputed in dierent lo ations Fig. A.3. TheC grid is onsidered more suitable than the other grids for the implementationof semi-impli it time dieren ing but Coriolis terms need to be averaged inboth horizontal dire tions, risking to redu e the amplitude of these two termson small s ales.Figure A.3: Arakawa C grid

115D gridAlso the Arakawa D grid is a fully staggered grid.Figure A.4: Arakawa D grid

E gridThe arakawa E grid is a semi staggered grid that looks like the B grid butthe lo ations are rotated through 45 degrees.Figure A.5: Arakawa E grid

116 The Arakawa Grids

Appendix BTurbulen e Closure ModelsIn o ean models, whi h mostly all assume the hydrostati approximation,there is the need to parameterize the non-hydrostati ee ts. These are onsidered sub-s ale pro esses whi h are mainly of onve tive and turbulentnature (Bur hard and Petersen, 1999).The Navier-Stokes equations an des ribe the more relevant pro esses of hy-drodynami s but a dierent approa h is needed to deal with the turbulen e,due to non-linear instabilities.B.1 EquationsThe Navier-Stokes equation of motion an be written as

∂tvi + vj∂jvi − ν∂jjvi + 2ǫijlΩjvl = −∂ip

ρ0

− gi

ρ0

ρ (B.1)with v velo ity, i j l indi es of artesian system, t time, ρ potential density, ρ0referen e density, p pressure, ν kinemati vis osity, Ωi = (0,Ωcos(Φ),Ωsin(Φ))rotation and gi = (0, 0, g) gravitation.ǫijl is the alternating tensor, whi h hanges sign when two indi es are swit hed.Its value is 1 if the indi es are sequential (i.e. i=1, j=2, l=3 or i=2, j=3,l=1), -1 if they are not (i.e. i=2,j=1,l=3) and 0 if they are identi al.Following the so alled Reynold's de omposition, whi h denes ea h variableas omposed of a mean eld (U) and a u tuating one (U), knowing that〈U〉 = 0, the Averaged Reynolds equations an be written

118 Turbulen e Closure Models∂tvi + vj∂j vi − ∂j(ν∂j vi − 〈vj vi〉) + 2ǫijlΩj vl = −∂ip

ρ0

− gi

ρ0

ρ (B.2)Multiplying ea h term of Eq.B.2 for v and knowing that e = 12v2, the energyequation an be obtained

∂te+ ∂j(vje+ vi〈vivj〉 − ν∂je+vj p

ρ0) = 〈vivj〉∂jvi −

gv3ρ

ρ0− ν(∂j vi)

2 (B.3)Subtra ting Eq.B.2 from Eq.B.1, the se ond moments transport equation anbe written∂t〈vj vi〉 + ∂l(vl〈vj vi〉 + 〈vlvivj〉 − ν〈vj vi〉) (B.4)

=

Pij︷ ︸︸ ︷

−∂lvi〈vlvj〉 − ∂lvj〈vlvi〉−Ωij

︷ ︸︸ ︷

2Ωl(ǫilm〈vj vm〉 + ǫjlm〈vivm〉)

−

Bij

︷ ︸︸ ︷

1

ρ0gi〈vjρ〉 + gj〈viρ〉−

Πij

︷ ︸︸ ︷

1

ρ0(〈vi∂j p+ vj∂ip〉)−

ǫij

︷ ︸︸ ︷

2ν〈(∂lvj)(∂lvi)where Pij is the shear produ tion, Ωij the redistribution due to rotation, Bijthe buoyan y produ tion, Πij the pressure strain orrelator and ǫij the dis-sipation of the Reynold stress 〈vivj〉.In a parallel way of the one presented above, the turbulent kineti energyequation an be obtained from Eq.B.4, imposing i = j and noting that theTKE an be written as k = 12〈v2

i 〉

∂tk + ∂j(vj + 〈vj1

2v2

i 〉 − ν∂jk +1

ρ0

〈vj p〉) =

P︷ ︸︸ ︷

−〈vj vi〉∂ivj

B︷ ︸︸ ︷

− g

ρ0

〈v3ρ〉ǫ

︷ ︸︸ ︷

−ν〈(∂j vi)2〉(B.5)with P shear produ tion, B buoyan y produ tion and ǫ dissipation rate ofturbulent kineti energy.The presented pro edure in extra ting the above equations is the one-point losure explained in Bur hard (2002). In the next se tion it is explained howthe TKE equation and the dissipation rate equation denition is needed to ompute a value for the verti al eddy vis osity.

B.2 Turbulen e parameterization 119B.2 Turbulen e parameterizationThe verti al eddy vis osity has to be dened if there is the intent to modelthe turbulen e ee ts, in order to solve the previous equations with a para-meterization , obtaining the velo ity s ale q and the lenght s ale l from them.Many dierent approa hes have been performed to parameterize the turbu-lent ee ts. This parameterization an be treated with dierent approa hes,applying an algebrai formulation, 1 equation or 2 equation models.B.2.1 Algebrai approa hThis approa h omputes the turbulent kineti energy k and the length l fromalgebrai relations. The algebrai equation for k is extra ted from a simpliedform of the transport equation of the turbulent kineti energy. The equationfor the length-s ale an have dierent formulations, ea h of them generallybased on empiri al motivations. Algebrai models are a over-simpli ationin numerous situations (Bur hard, 2002).B.2.2 1 equation modelsThe omputation of k is done with the dierential transport equation for theturbulent kineti energy (Eq.B.4). On e more, even in this ase, the length-s ale is omputed from an empiri ally or theoreti ally based relation. Havingthe value of l, the dissipation rate ǫ is then re al ulated by means ofl = cL

k3/2

ǫ(B.6) alled Kolmogorov relation, with cL = (c0µ)3/4 ma ro length s ale for energy- ontaining eddies.This is a possible approa h and leads to the denition of eddy vis osity νtand diusivity ν ′t as follows

νt = cνk2

ǫν ′t = c′ν

k2

ǫ(B.7)It is widely adopted in geophysi al models (Bur hard, 2002).

120 Turbulen e Closure ModelsB.2.3 2 equation modelsIn this kind of models, both k and l are omputed from the dierentialtransport equations. As it happens in the 1 equation models, k is obtainedfrom the transport equation of the turbulent kineti energy. Also the length-s ale is determined from a dierential transport equation. There are dierentapproa hes in determining the kind of equation to be used for the length s ale omputation and this is the main dieren e between the models presentedbelow. The variable an be obtained from the rate of dissipation, ǫ, or fromthe produ t kl (Bur hard, 2002).In the following, basi information about the more used 2 equation models isgiven. Many dis ussion raised around the problem of the hoi e of the rightequations to ompute the length s ale, with, mainly, two dierent approa hes.Mellor-Yamada modelMellor and Yamada (1974), as a rst step, proposed an algebrai solutionfor the omputation of the ma ro turbulen e length s ale. After that, theydeveloped a prognosti transport equation for kL∂t(kL) − ∂z(Sl

√2kL∂z(kL)) =

L

2[E1P + E3B − (1 + E2(

L

Lz)2ǫ)] (B.8)with Sl stability fun tion and B1, E1, E2, E3 parameters (Bur hard, 2002).They also introdu ed a modied TKE equation

∂t(k) − ∂z(Sq

√2kL∂z(k)) = P + B − ǫ (B.9)where Sq, onstant stability fun tion, is set to permit a higher entrainmentthrough the density interfa es. The presen e of Sq and the absen e of thevis ous mixing term, are two hara terizing aspe ts of the Mellor-YamadaModel.k-ǫ modelThis is the model applied introdu ing the GOTM into the SHYFEM stru -ture.The ǫ equation has to be expressed in a exa t form and to a hieve this inthe terms present on the right hand side of the equation parameters areintrodu ed as losure assumptions taken from theory and observations by alibration. The losed ǫ equation is

B.2 Turbulen e parameterization 121∂tǫ− ∂z((ν +

νt

σǫ

)∂zǫ) =ǫ

k(c1ǫP + c3ǫB − c2ǫǫ) (B.10)with c1ǫ,c2ǫ,c3ǫ,σǫ as parameters. If c2ǫ is alibrated taking in onsiderationthe freely de aying homogeneous turbulen e behind a grid the k equation,for long integration times, an be determined as a power law,

k

k0= A(

t

τ0)d (B.11)

d de ay rate, A onstant parameter, k0 initial turbulent kineti energy andτ0 turbulent time s ale. c1ǫ, c3ǫ and σǫ an be determined in many dierentways, here not treated.What has to be stressed is that, in this ase, the equation for small s aleturbulen e is used to determine the ma ro length s ale and this is one of the entral points in the big dis ussion raised around the physi al relevan e ofdierent models. Mellor and Yamada (1982) used this argument to supportthe k-kL model, where there is onsisten y in the treatment of the ma rolength s ale. On the other hand, Rodi (1987) stressed how the nature ofboth ǫ and kL equations are fairly empiri al and how it is not a matter ofphysi al relevan e but, more, of parameterization. No general dieren es arein the use of one of the two models approa h but in the Mellor and Yamada(1974) model, the kL equation needs one more near wall term.

122 Turbulen e Closure Models

A knowledgementsI want to gratefully a knowledge my tutor, Dr. Georg Umgiesser, who in-trodu ed me in this weird world that is S ienti Resear h. Thanks for thehelp and the respe t given to someone who is just a beginner.Thanks to Professor Nadia Pinardi and Professor Antonio Navarra, for thes ienti and nan ial support, both fundamental.Thanks to Professor Alberto Tomasin, the "Lord of Tides", for the pre ioustime spent dis ussing about tides, surge and sei hes.Thanks to Dr. John Warner, from USGS, for the dis ussions on modeling andthe great opennes in working on model omparison and thoroughly revisingsimulation results.Thanks to Dr. Andrea Cu o, Dr. Christian Ferrarin, Mar o Bajo and,parti ularly, to Fran es a De Pas alis and Dr. Mi hol Ghezzo, whi h are the olleagues I worked with during these years, for the professional and, aboveall, personal, support.Thanks to Dr. Katrin S hroeder be ause she enlarged my s ienti thoughtsfrom the shallow waters to the deep sea...hoping to go far!Thanks to Dr. Alessandro Sarretta for the sin ere support and for the helpwith GIS and with the emendation of this work.Thanks to Dr. Vedrana Kova£evi¢ and Isaa Man ero Mosquera that pro-vided the HF Radar and that helped me in dis ussing the riti ity of someresults.Thanks for the partial funding to Dr. Cosimo Solidoro.Thanks to CMCC - Centro Euromediterraneo per i Cambiamenti Climati i,that partially funded this work.Thanks to INGV for the MFStep data used in this work.Thanks to CORILA proje ts 3.2Hydrodynami s and morphology of the Veni eLagoon and 3.5Quantity and quality of ex hanges between lagoon and sea thatprovided the ux data.

124 A knowledgementsThanks to the Veni e Muni ipality that provided the wind and sea level data.

BibliographyArakawa, A. and Lamb, V. R. (1994). Computational Design of the Basi Dynami al Pro esses of the UCLA General Cir ulation Model. Methods ofComputational Physi s, 17:173265.Artegiani, A., Bregant, D., Pas hini, E., Pinardi, N., Rai i h, F., and Russo,A. (1997a). The Adriati Sea General Cir ulation. Part I: Air-Sea In-tera tion and Water Mass Stru ture. Journal of Physi al O eanography,27:14921514.Artegiani, A., Bregant, D., Pas hini, E., Pinardi, N., Rai i h, F., and Russo,A. (1997b). The Adriati Sea General Cir ulation. Part II: baro lini ir- ulation stru ture. Journal of Physi al O eanography, 27:15151532.Artegiani, A., Ga£i¢, M., Mi helato, A., Kova£evi¢, V., Russo, A., Pas hini,E., S arazzato, P., and Smirmi , A. (1993). The Adriati Sea hydrographyand ir ulation in spring and autumn (1985-1987). Deep Sea Resear h,II(40):11431180.Bajo, M., Zampato, L., Umgiesser, G., Cu o, A., and Canestrelli, P. (2007).A nite element operational model for the storm surge predi tion in Veni e.Estuarine, Coastal and Shelf S ien e, 75:236249.Barron, C. H., Birol Kara, A., Martin, P. J., Rhodes, R. C., and Smedstad,L. F. (2006). Formulation, implementation and examination of verti al oordinate hoi es in the Global Navy Coastal O ean Model (NCOM).O ean Modelling, 11:347375.Bellaore, D., Umgiesser, G., and Cu o, A. (2008). Modelling the waterex hanges between the Veni e Lagoon and the Adriati Sea. O ean Dy-nami s, 58:397413.Bergamas o, A., Carniel, S., Pastres, R., and Pe enik, G. (1998). A uniedapproa h to the modelling of the Veni e Lagoon-Adriati Sea e osystem.Estuarine, Coastal and Shelf S ien e, 46:483492.

126 BIBLIOGRAPHYBergamas o, A., Oguz, T., and Malanotte-Rizzoli, P. (1999). Modeling densewater formation and winter ir ulation in the northern and entral Adriati Sea. Journal of Marine Systems, 20:279300.Bian hi, F., Ravagnan, E., A ri, F., Bernardi-Aubry, F., Boldrin, A., Ca-matti, E., Cassin, D., and Tur hetto, M. (2004). Variability and uxes ofhydrology, nutrients and parti ulate matter between the Veni e Lagoonand the Adriati Sea. Preliminary results (years 2001-2002). Journal ofMarine Systems, 51(v-vi):4964.Blumberg, A. F. and Mellor, G. L. (1987). A des ription of a three-dimensional oastal o ean ir ulation model. In Heaps, N. S., editor,Three-dimensional Coastal O ean Models. Coastal and Estuarine S ien e,volume 4, pages 116, Washington D.C. Ameri an Geophysi al Union.Bur hard, H. (2002). Applied Turbulen e Modelling in Marine Waters.Springer, Berlin Heildelberg.Bur hard, H. and Petersen, O. (1999). Models of turbulen e in the marineenvironment - a omparative study of two equation turbulen e models.Journal of Marine Systems, 21:2953.Castellari, S., Pinardi, N., and Leaman, K. (1998). A model study of theair-sea intera tions in the Mediterranean Sea. Journal of Marine Systems,18:89114.Cavaleri, L. and Bertotti, L. (1996). In sear h for the Corre t Wind and WaveFields in a Minor Basin. Monthly Weather Review, 125(8):19641975.Cavaleri, L., Piantá, and Iuso, G. (1984). Inuen e of Sea Stru ture on thesurrounding Wind Field. Il Nuovo Cimento, 7C(4):441446.Chao, S. and Boi ourt, W. C. (1986). Onset of Estuarine Plumes. Journalof Physi al O eanography, 16:21372149.Chorin, A. J. (1967). A numeri al method for solving in ompressible vis ousow problems. Journal of Computational Physi , 2:1226.Crise, A., Cavazzon, F., Mala£i¢, V., and Querin, S. (2003). Cir olazioneIndotta dal Vento di Bora nel Golfo di Trieste: Studio Numeri o in Con-dizioni di Strati azione. In La difesa idrauli a del territorio 2003.Cu o, A. and Umgiesser, G. (2005). Modeling the tide indu ed water ex- hanges between the Veni e Lagoon and the Adriati Sea. In S ienti

BIBLIOGRAPHY 127Resear h and Safeguarding of Veni e. Pro eedings of the Annual Meetingof the CORILA Resear h Program, 2003 Results, volume III, pages 385402, Veni e, Italy.Cu o, A. and Umgiesser, G. (2006). Modeling the Veni e Lagoon Residen eTime. E ologi al Modelling, 193(1-2):3451.Cushman-Roisin, B., Korotenko, K., and Dietri h, D. E. (2005). Simulationand Charaterization of the Adriati Sea Mesos ale Variability. Journal ofGeophysi al Resear h - O eans, Spe ial Adriati Sea Issue.Cushman-Roisin, B. and Naimie, C. E. (2002). A 3D-nite element modelfor the Adriati tides. Journal of Marine Systems, 37(4):279297.Fairall, C., Bradley, F. F., Godfrey, J. S., Wi k, G. A., and Edson, J. B.(1996). Cool-skin and warm-layer ee ts on sea surfa e temperature. Jour-nal of Geophysi al Resear h - O eans, 101:12951308.Ferla, M., Cordella, M., Mi hielli, L., and Rus oni, A. (2007). Long-termvariation on the sea level and the tidal regime in the lagoon of Veni e.Estuarine, Coastal and Shelf S ien e, 75:214222.Fofono, N. P. (1985). Physi al properties of seawater: a new salinity s aleand equation of state for seawater. Journal of Geophysi al Resear h -O eans, 90(C2):33323343.Foreman, M. G. G. (1978). Manual for tidal urrents analysis and predi tion.Pa i Marine S ien e Report 78-6, Institute of O ean S ien es, Patri iaBay, Sydney, British Columbia.Foreman, M. G. G. (1996). Manual for tidal heights analysis and predi tion.Pa i Marine S ien e Report 77-10, Institute of O ean S ien es, Patri iaBay, Sydney, British Columbia.Fran o, P., Jefti¢, L., Rizzoli, P. M., Mi helato, A., and Orli¢, M. (1982).Des riptive model of the Northern Adriati . O eanologi a A ta, 5(3).Friedri h, H. and Levitus, S. (1972). An approximation of the equationof state for sea water, suitable for numeri al o ean models. Journal ofPhysi al O eanography, 2:514517.Gatto, P. (1984). Il ordone litoraneo della laguna di Venezia e le ause delsuo degrado. Istituto Veneto di S ienze, Lettere ed Arti - Rapporti e Studi,IX:163193.

128 BIBLIOGRAPHYGa£i¢, M., Kova£evi¢, V., Mazzoldi, A., Paduan, J. D., Man ero Mosquera, I.,Gelsi, G., and Ar ari, G. (2002). Measuring Water Ex hange between theVenetian Lagoon and the open sea. Eos, Transa tion, Ameri an Physi alUnion, 83(20).Ga£i¢, M., Man ero Mosquera, I., Kova£evi¢, V., Mazzoldi, A., Cardin, V.,and Gelsi, F. (2004). Temporal variation of water ow between the Vene-tian lagoon and the open sea. Journal of Marine Systems, 51.Goldmann, A., Rabagliati, R., and Sguazzero, P. (1975). Chara teristi s ofthe Tidal Wave in the Lagoon of Veni e. Te hni al Report 47, IBM, Veni eS ienti Center.Haidvogel, D. B., Arango, H. G., Hedstrom, K., Be kmann, A., MalanotteRizzoli, P., and Sh hepetkin, A. F. (2000). Model Evaluation Experimentsin the North Atlanti Basin: Simulations in Nonlinear Terrain-FollowingCoordinates. Dynami s of Atmospheres and O eans, 32:239281.Kato, H. and Phillips, O. (1969). On the penetration of a turbulent layerinto stratied uids. Journal of Fluid Me hani s, 37:643655.Kondo, J. (1975). Air-Sea bulk transfer oe ients in diabati onditions.Boundary Layer Meteorol., 9:91112.Kourafalou, V. (1999). Pro ess studies on the po river plume, north adriati sea. Journal of Geophysi al Resear h, 104(C2):2996329985.Kourafalou, V. (2001). River plume development in semi-en losed Mediter-ranean regions: North Adriati and Northwestern Aegean Sea. Journal ofMarine Systems, 30:1812005.Kova£evi¢, V., Ga£i¢, M., Mosquera, I. M., Mazzoldi, A., and Marinetti, S.(2004). Hf radar observation in the northern Adriati : surfa e urrent eldin front of the Venetian Lagoon. Journal of Marine Systems, 51(1-4):95122.Luyten, P., Deleersnijder, E., Ozer, J., and Ruddi k, K. (1996). Presentationof a family of turbulen e losure models for stratied shallow water owsand preliminary appli ation to the Rhine outow region. Continental ShelfResear h, 16(1):101130.Luyten, P. J., Jones, J. E., Pro tor, R., Tabor, A., Tett, P., and Wild-Allen,K. (1999). COHERENS - a oupled Hydrodynami al-E ologi al Model forRegional and Shealf Seas: User Do umentation. Report, MUMM.

BIBLIOGRAPHY 129Malanotte Rizzoli, P. and Bergamas o, A. (1983). The Dynami s of the oastal region of the Northern Adriati Sea. Ameri al Meteorologi al So- iety, 13:11051130.Mala£i¢, V., Viezzoli, D., and Cushman-Roisin, B. (2000). Tidal dynami sin the northern Adriati Sea. Journal of Geophysi al Resear h - O eans,105(C11):26,26526,280.Man ero Mosquera, I., Ga£i¢, M., Kova£evi¢, V., Mazzoldi, A., Paduan,J. D., and Yari, S. (2007). Surfa e urrent patterns in front of the Venetianlagoon and their variability at dierent wind regimes. In S ienti Resear hand Safeguarding of Veni e - CORILA Resear h Programme 2004-2006,volume VI, pages 441451, Veni e, Italy.Marinov, D., Norro, A., and Zaldivar, J. M. (2006). Appli ation of CO-HERENS model for hydrodynami investigation of Sa a di Goro oastallagoon (Italian Adriati Sea). E ologi al Modelling, 193:5268.Marshall, J., Ad roft, A., Hill, C., L., P., and Heisey, C. (1997). A nite-volume, in ompressible Navier Stokes model for studies of the o ean on par-allel omputers. Journal of Geophysi al Resear h - O eans, 102(C3):57535766.Melaku Canu, D., Umgiesser, G., and Solidoro, C. (2001). Short term simu-lations under winter onditions in the lagoon of Veni e: a ontribution tothe environmental impa t assessment of a temporary losure of the inlets.E ologi al Modelling, 138(13):215230.Mellor, G. L. (1991). An equation of state for numeri al models of o ean andestuaries. J. Atmos. O eani Te hnol., 8:609611.Mellor, G. L. and Yamada, T. (1974). A hierar hy of turbulen e losuremodels for planetary boundary layers. Journal of Atmospheri S ien e,31:17911806.Mellor, G. L. and Yamada, T. (1982). Development of a tubulen e losuremodel for geophysi al uid problems. Reviews of Geophysi s and Spa ePhysi s, 20(4):851875.Mosetti, F. (1987). Distribuzione delle maree nei mari italiani. Bollettino diO eanologia Teori a ed Appli ata, 5(1):6572.Oddo, P. and Pinardi, N. (2008). Lateral open boundary onditions fornested limited area models: A s ale sele tive approa h. O ean Modelling,20:134156.

130 BIBLIOGRAPHYOddo, P., Pinardi, N., and Zavatarelli, M. (2005). A numeri al study of theinterannual variability of the Adriati Sea. S ien e of the Total Environ-ment, 353:3956.Orli¢, M., Ga£i¢, M., and Violette, P. E. L. (1992). The urrents and ir u-lation of the Adriati Sea. O eanologi a A ta, 15:109124.Paduan, J. D., Ga£i¢, M., Kova£evi¢, V., Mosquera, I. M., and Mazzoldi, A.(2003). Vorti ity Pattern Oshore of the Venetian Lagoon from HF RadarObservations. In S ienti Resear h and Safeguarding of Veni e - CORILAResear h Programme 2001-2003, volume II, pages 361372, Veni e, Italy.Pasari¢, M. and Orli¢, M. (2001). Long-term meteorologi al pre onditioningof the North Adriati oastal oods. Continental Shelf Resear h, 21:263278.Pinardi, N., Allen, I., Demirov, E., Mey, P. D., Korres, G., Traon, P. L.,Maillard, C., Manzella, G., and Tziavos, C. (2003). The mediterraneano ean fore asting system: rst phase of the implementation (1998-2001).Annales Geophysi ae, 21:118.Pirazzoli, P. and Tomasin, A. (2002). Wind and atmospheri pressure inVeni e in the 20th entury: a omparative analysis of measurements fromthe meteorologi al stations of the Seminario Patriar ale (1900-1955) andthe Istituto Cavanis (1959-2000). Atti dell'Istituto Veneto di S ienze, Let-tere ed Arti, CLX.Polli, S. (1960). La propagazione delle maree nellÁlto adriati o. Publi ationsof the Istituto Sperimentale Talassogra o - Trieste, 370.Polli, S. (1961). La propagazione delle maree nel golfo di Venezia. Publi a-tions of the Istituto Sperimentale Talassogra o - Trieste, 385.Pullen, J., Doyle, J. D., Hodur, R., Ogston, A., and Book, J. W. (2003).Coupled o ean-atmosphere and nested modeling of the Adriati Sea dur-ing winter and spring 2001. Journal of Geophysi al Resear h - O eans,108(C1,3320).Rai i h, F. (1994). Note on the ow rates of the Adriati rivers. Te hni alReport RF 02, Istituto Sperimentale Talassogra o-CNR, Trieste, Italy.Rasmussen, E. B. (1993). Three-dimensional hydrodynami models, pages12951308. Chapman and Hall, London.

BIBLIOGRAPHY 131Ro hford, P. A. and Martin, P. J. (2001). Boundary onditions in the NavyCoastal O ean Model. Report nrl/fr/7330-01-9992, Nav. Res. Lab, StennisSpa e Cent., Miss.Rodi, W. (1987). Examples of al ulation methods for ow and mixing instratied uids. Journal of Geophysi al Resear h (C5), 92:53055328.Sannino, G. M., Barbagli, A., and Artale, V. (2002). Numeri al Modeling ofthe mean ex hange through the Strait of Gibiltar. Journal of Geophysi alResear h - O eans, 107(Ant 3094).S iarra, R., Bignami, F., Santoleri, R., and Carniel, S. (2006). The variabilityof the Adriati Sea Case 2 waters from SeaWiFS imagery. submitted toJournal of Geophysi al Resear h - O eans [In Press.Sherwood, C. R., Carnie, S., Cavaleri, L., Chiggiato, J., Das, H., Doyle,J. D., Harris, C. K., Niedoroda, A. W., Pullen, J., Reed, C. W., Russo,A., S lavo, M., Signell, R. P., Traykowski, P., and Warner, J. C. (2004).Sediment Dynami s in the Adriati Sea Investigated with Coupled Models.O eanography, 17(4):5869.Signell, R. P., Carniel, S., Cavaleri, L., Chiggiato, J., Doyle, J. D., Pullen,J., and S lavo, M. (2005). Assessment of wind quality for o eanographi modelling in semi-en losed basins. Journal of Marine Systems, 53:217233.Smolarkiewi z, P. K. (1984). A fully multidimensional positive denite sd-ve tion transport algorithm with small impli it diusion. Journal of Com-putational Physi s, 54:325362.Smolarkiewi z, P. K. and Clark, T. L. (1986). The multidimensional positivedenite sdve tion transport algorithm: further development and appli a-tions. Journal of Computational Physi s, 67:396438.Tomasin, A. (2005). The software Polifemo for tidal analysis. Te hni al Note202, ISMAR-CNR Institute of Marine S ien e Veni e.Tomasin, A. and Pirazzoli, P. A. (1999). The Sei hes in the Adriati Sea.Atti dell'Istituto Veneto di S ienze, Lettere ed Arti, CLVII:299316.Umgiesser, G. (2000). Modeling residual urrents in the Veni e Lagoon. InIntera tion between Estuaries, Coastal Seas and Shealf Seas, pages 107124. Terra S ienti Publishing Company (TERRAPUB), Tokyo.

132 BIBLIOGRAPHYUmgiesser, G. and Bergamas o, A. (1993). A staggered grid nite ele-ment model of the Veni e Lagoon. In K. Morgan, E. Oate, J. P. andZienkiewi z, O., editors, Finite Elements in Fluids, pages 659668. Piner-idge Press.Umgiesser, G. and Bergamas o, A. (1995). Outline of a primitive equationnite element model. In Rapporto e Studi, volume XII, pages 291320.Istituto Veneto di S ienze, Lettere ed Arti, Veni e, Italy.Umgiesser, G. and Bergamas o, A. (1998). The spreading of the Po plumeand the Italian oastal urrent. In Physi s of Estuaries and Coastal Seas,pages 267275. Dronkers and S heers (eds), Rotterdam.Umgiesser, G., Melaku Canu, D., Cu o, A., and Solidoro, C. (2004). A niteelement model for the Veni e Lagoon. Development, set-up, alibrationand validation. Journal of Marine Systems, 51:123145.Vested, H. J., Berg, P., and Uhrenholdt, T. (1998). Dense water formationin the Northern Adriati . Journal of Marine Systems, 18:135160.Williams, R. T. (1981). On the Formulation of Finite-Element Predi tionModels. Monthly Weather Review, 109:463.Zampato, L., Canestrelli, P., A.Tomasin, and Ze hetto, S. (2005). A ompar-ison between modelled and observed atmospheri elds over the Adriati and Tyrrhenian seas. Te hni al Report 263, ISMAR-CNR, Venezia, Italy.Zampato, L., Umgiesser, G., and Ze hetto, S. (2007). Sea level fore astingin Veni e through high resolution meteorologi al elds. Estuarine, Coastaland Shelf S ien e, 75:223235.Zavatarelli, M. and Pinardi, N. (2003). The Adriati Sea modelling system:a nested approa h. Annales Geophysi ae, 21:345364.Zavatarelli, M., Pinardi, N., Kourafalou, V. H., and Maggiore, A. (2002).Diagnosti and prognosti model studies of the Adriati Sea general ir- ulation: Seasonal variability. Journal of Geophysi al Resear h - O eans,107(C1,3004).